Hector circled the walls of Troy three times while fleeing from Achilles. This pursuit occurs in Book 22 of the Iliad, immediately before their final confrontation and Hector’s death.
Hector had returned to the battlefield after the Trojan army retreated, but once Achilles approached, fear overcame his resolve. He ran around the city’s walls while Achilles pursued him. Apollo repeatedly strengthened Hector so that Achilles could not catch him, yet the god could not prevent the encounter’s destined ending.
The chase is sometimes confused with Achilles’ later treatment of Hector’s corpse. After the killing, Achilles fastened the body to his chariot and dragged it around the Achaean camp and Patroclus’ burial mound. That was a separate act. The three circuits refer specifically to Hector’s flight before the duel, not to the corpse’s later dragging.