Final answer:
Katniss Everdeen ends Cato's suffering by shooting him in the head with an arrow after he is mauled by muttations, following an intense fight on the Cornucopia in The Hunger Games.
Step-by-step explanation:
In the novel The Hunger Games by Suzanne Collins, Katniss Everdeen kills Cato in a humane way to spare him from further suffering. After an intense battle atop the Cornucopia where Cato has Peeta in a headlock, threatening to kill him, Katniss shoots Cato with an arrow. However, it's not this arrow that kills him; it's the muttations (mutant creatures) below that maul him. To finally put Cato out of his misery after hearing his prolonged suffering, Katniss shoots him one more time with an arrow aimed at his head, leading to his death.