Final answer:
During the Trojan War, there was a quarrel between Achilles and Agamemnon over a captured Trojan princess. This dispute resulted in Achilles withdrawing from battle and refusing to fight for the Greeks.
Step-by-step explanation:
The quarrel between Achilles and Agamemnon occurred during the Trojan War as depicted in Homer's Iliad. Achilles and Agamemnon had a dispute over a prize of honor, which was the captured Trojan princess, Briseis. Agamemnon took her from Achilles as compensation for having to return his own war prize, Chryseis. This led to Achilles withdrawing from battle and refusing to fight for the Greeks, which had significant consequences in the war.