Mùróng ShàoZōng then turned his forces against Hóu Jĭng, and their forces fought at GuōYáng (present day MengCheng, AnHui Province). Hóu Jĭng ordered his troops to enter the fray in shorter armour and wielding short swords, to hamstring the enemy troops and their horses, and defeated the enemy. Subordinates of Mùróng ShàoZōng, Húlü Guāng fled while Zhāng ShìXiăn was captured after falling from his horse.
Mùróng ShàoZōng lamented he had not encountered such a difficult foe to overcome like Hóu Jĭng, and decided to play for time and withdrew to the city of Qiáo (present day NE Shangqiu in HeNan Province). Hóu Jĭng tried unsuccessfully to assault it and had to withdraw to GuōYáng. After a couple of months of standoff, Hóu Jĭng ran out of provisions.
In the first month of the following year (AD 548), Mùróng ShàoZōng launched a pincer attack with 5,000 armoured cavalry against Hóu Jĭng. Some of Hóu Jĭng's subordinates, including Bào Xiăn, surrendered to Mùróng ShàoZōng. Hóu Jĭng was beaten and forced to flee. Mùróng ShàoZōng scored a great victory, capturing or killing more than 50,000 opponents.
After regrouping, Hóu Jĭng led the remnants of his forces, 800 infantry and cavalry, to seek refuge in the city of ShòuYáng of Southern Liáng (present day Shou county of AnHui province). Despite the great fall in his "value" (with neither land nor troops to offer), Hóu Jĭng was accepted by Southern Liáng.
I've checked, and Qiao city 谯城 was actually present-day Haozhou city in Anhui, a little south of Shangqiu in Henan.
Here is a fuller account (from the Zizhi Tongjian) of the Battle of Hanshan between Murong Shaozong and the Liang army, and the Battles of Guoyang between Hou Jing and Murong Shaozong, showing why Hou Jing lost in the end:
The wily Murong Shaozong had inflicted a catastrophic defeat on Xiao Yuanming's Liang army at Hanshan (or Mount Han), capturing Xiao Yuanming and generals Hu Guisun and Zhao Bochao, by conducting a risky feigned retreat using psychological warfare. Aware that the morale of the Liang army was high and its offensive power greater than his, he instructed his troops before the assault on the Liang camp: "I will order a feigned retreat so as to draw those southerners in deep. Once that has happened, surround them and hit them hard!" In the initial assault, Murong Shaozong only sent in 10,000 of his total of 100,000 troops. They were repelled with a loss of 200 men by the Liang general Hu Guisun, despite Xiao Yuanming being drunk and unable to lead the army, and also the refusal of Zhao Bochao to join in the battle. But once the Liang troops threw themselves into pursuing the Eastern Wei force, the Wei soldiers believed that everything was indeed unfolding according to Murong Shaozong's plan, and turned around and charged eagerly at the Liang army. At this point, Murong probably unleashed the remaining 90,000 of his troops, encircling the Liang army and crushing it. Next, Murong marched south and captured the Liang province of Tongzhou, whose governor abandoned his city after a short siege.
Hou Jing was at this time besieging the city of Qiao, to the west along the Guo River (a tributary of the Huai). Failing to take Qiao, he moved a short distance southeast and captured Chengfu, using it as his base. He then sent Wang Wei, his secretary, to Xiao Yan in Jiankang, urging Xiao to install one of the exiled Wei princes in the south as the new Wei emperor so as to undermine the legitimacy of the Eastern Wei and the Gao regime. Xiao Yan readily agreed and appointed the exiled prince Yuan Zhen as the rightful Wei emperor, giving him an army and promising to recognise his rule once he had conquered the north. Yuan Zhen was the son of Yuan Shu, a Northern Wei prince who had fled to the Liang in 501 after his father Yuan Xi was executed for plotting treason. In 532, Yuan Shu was captured by a besieging Wei army in (guess what) the city of Qiao. He was taken to Luoyang and finally executed when he tried to escape south again. The Liang court was confident that Yuan Zhen, who had remained in the south, would be a loyal puppet to use against the Wei dynasty that had killed his father and grandfather.
Murong Shaozong now moved to attack Hou Jing in full force. Hou withdrew further south along the Guo River, from Chengfu to Guoyang. He sent an envoy to Murong, asking, "Are you here to see me off, or to force a showdown?" Murong replied, "I am resolved to fight it out with you!" Murong set up camp with his army's backs to the wind, so as to increase the range of his arrows and use fire against Hou Jing. Hou was aware of this and declined to engage in battle until the wind had died down. Murong told his commanders, "Hou Jing is a crafty fellow who likes to use flanking and encircling tactics." He thus ordered his rear to be on full alert. Sure enough, Hou Jing launched a strike at Murong's rear, but there was one surprise that Murong had not anticipated. Hou Jing ordered all his troops to wear only upper body armour, without the usual skirting, and wield short blades, bending low and charging into the Eastern Wei lines to chop at the legs of enemy soldiers and horses. The Eastern Wei lines collapsed, and Murong Shaozong himself fell when his horse was chopped. His subordinate Liu Fengsheng was injured, while Zhang Zunye was captured.
Murong and Liu Fengsheng retreated to Qiao, where junior generals Hulu Guang and Zhang Shixian greeted them with indignation at their having been defeated by an army less than half their size (Hou Jing had only 40,000 troops to Murong's 100,000, and only a few thousand horses - hence his decision to use the unorthodox leg-chopping tactic rather than a standard cavalry clash). Murong Shaozong said to the two generals, "I've been in many battles, but have never met an opponent as tough as Hou Jing. You two can go and try him if you wish." Hulu and Zhang thus put on their armour and prepared to go and fight Hou Jing. Murong warned them, "Do not cross the Guo River." (Hou Jing was in Guoyang, on the south bank of the river, while Qiao was to the west on the north bank)
Hulu and Zhang thus set up camp on the north bank of the river, and Hulu Guang rode an unarmoured horse to the river bank to shoot arrows across the river at Hou Jing's camp as a challenge. Hou rode to the river and said to Hulu, "You come thirsting for glory, but I am heading south simply because I fear death. I am an old friend of your father (Hulu Jin), so why are you shooting at me? How did you know not to cross the river? It must have been Murong Shaozong who taught you that." Hulu Guang could make no reply. Hou then ordered his officer Tian Qian to shoot Hulu's horse. With a single arrow, Tian pierced the chest of Hulu's horse. Hulu hurriedly mounted another horse and took cover behind a large tree. Tian shot again, and this time the arrow pierced both the tree and the horse! Hulu was shocked and fled back to his camp. But Zhang Shixian was foolhardy enough to cross the river and attack Hou, and was captured. Hou then released him. When they returned to Qiao, Murong Shaozong saw the look on their faces and asked, "Well, what do you think now? Am I to be blamed for losing?"
Duan Shao, another of Gao Huan's great generals, tried using a fire attack on Hou's camp. He set up camp on both sides of the Guo River, and sent troops to set fire to the grass near Guoyang. But Hou Jing simply led his cavalry into the river and then back out onto the grass, and the water on the horses' hooves, as well as that splashed up by the horses, extinguished the flames.
However, Hou Jing's brilliance could not prevent the steady diminishing of his supplies as he carried out a standoff with Murong Shaozong along the Guo River throughout the winter of 547. One week after the Chinese New Year in 548, Murong Shaozong judged that the time was right. He led 5,000 elite troops in a pincer attack on Guoyang. In order to rally his demoralised troops to fight, Hou Jing called out to them that Gao Cheng had executed their families. But Murong Shaozong called to them from his own army, saying, "Your families are alive and well, and if you return to us, your official positions and titles will be retained as they are." He took off his helmet, letting his hair hang loose, and faced the Big Dipper to swear that his words were true. Hou Jing's troops had mostly been reluctant to head south, and many were now convinced by Murong Shaozong to defect. Bao Xian, a governor who had originally been captured by Hou Jing in the first place, led his troops to return to Murong Shaozong's side, along with some other generals. Hou Jing's army fell apart, and large numbers of his troops streamed northward to try and cross the Guo River, hoping to return to the north. Most of them drowned, such that the flow of the river was dammed up by corpses.
Hou Jing, along with a handful of his trusted generals, fled south across the Huai River, and managed to gather 800 remaining troops. They passed by a small town, in which one of the residents mocked him saying, "Hey you cripple, what are you going to do now?" Hou was very sensitive about his right leg being shorter than his left, so he flew into a rage and captured the town just so he could kill the person who had insulted him. Murong Shaozong's army did not dare to pursue Hou too closely, for fear of Liang reinforcements or traps. Also, Hou sent a message to Murong, saying, "If I am destroyed, what further use will Gao Cheng have for you?" This made sense to Murong, who then allowed Hou to escape.