苦しみを楽にしてあげるを英語でなんと言うか？

put out of one's misery には安楽死させる、殺してあげることで楽にしてやるという、意味があります。 0:37 they say they had no choice but to put the bleeding and panic-stricken bear out of his misery. 出血してパニックってる熊を殺すより仕方が無かったと警察は言う。

Bear frenzy in shopping mall: video
https://www.youtube.com/watch?v=OhbuMsGdn-Y  0:55 as for the victim's final moments, the Dell kept giving Hinch what he called the "blue screen of death" before he finally put it out of its misery. このデルコンピューターは撃たれる前にブルースクリーンとなったので、ヒンチ容疑者はやむなくこれを介錯してやった。
Man guns down his misbehaving computer

練習問題解答
a-3589 put him out of his misery
a-9110 put him out of his misery
b-2282 put you out of your misery
b-4469 put him out of his misery