Final answer:
Achilles kills Hector in the Trojan War by stabbing him through the neck with his spear.
Step-by-step explanation:
Achilles kills Hector in the epic poem The Iliad by Homer. In the story, Achilles is a great hero who is invincible except for his vulnerable heel. During the Trojan War, Achilles seeks revenge for the death of his close friend Patroclus and challenges Hector to single combat. Achilles ultimately defeats Hector and kills him by stabbing him through the neck with his spear.