Final answer:
The army turned around from Beit Nuba on 13 January 1192 due to challenges such as supply shortages, military tactics by Saladin, and unfavorable terrain and weather conditions.
Step-by-step explanation:
The army turned around from Beit Nuba on 13 January 1192 because they were facing significant challenges and obstacles. One reason was that the crusaders had been weakened by the long and difficult journey to Palestine, and they were running out of supplies.
The Egyptian sultan, Saladin, also employed various military tactics to cut off their access to food and water, making their situation increasingly dire. Additionally, the unfavorable terrain and harsh weather conditions made it difficult for the crusaders to sustain their campaign.