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哄的英文，一般說來是：

coax

任性的英文，應該是：

headstrong, obstinate, unruly (意義上都有不同，要看上下文來決定用法)

但是，哄小孩，或是哄女朋友，我會用 pamper的字眼。因為，其實就是安撫的意思，就像媽媽幫小孩包尿布一樣。雖然 pamper會有溺愛的意思在裡面。

供您參考喔。

哄有點騙的意思

所以有點像安慰使對方舒服一點

Comfort the baby with a new toy.

Comfort the girl with a gift.

任性=Wayward

I would use " pet"(verb) as 哄.

Eg. Just pet her nicely, so that she will do whatever it takes.

哄, Talk (someone) into...

任性 strongheaded, stubborn