Final answer:
The Trojan War, which lasted for 9 years, led to a quarrel between Agamemnon and Achilles over a captive woman named Briseis.
Step-by-step explanation:
The war that went on for 9 years and resulted in a quarrel between Agamemnon and Achilles is known as the Trojan War. It was a legendary conflict between the city of Troy and the Greeks, as depicted in the epic poem, the Iliad, written by Homer. The quarrel between Agamemnon, the leader of the Greek forces, and Achilles, the greatest Greek warrior, arose due to a dispute over a captive woman named Briseis. Agamemnon took her from Achilles, who felt dishonored and withdrew from the war. This conflict had a significant impact on the outcome of the war.