〜てほしい
Want someone to do somethingmachine translation
FormationPerson you want + に + verb て-form + ほしい
〜てほしい expresses wanting SOMEONE ELSE to do something: 母に休んでほしい (I want my mother to rest). The person you want takes the particle に, and the action is in the て-form plus ほしい; ほしい conjugates like an い-adjective.
Let's line up the three ways of saying "want" so they don't get mixed up: 〜がほしい (N5) — wanting to HAVE a thing (車がほしい); 〜たい (N5) — wanting to do something YOURSELF (行きたい); 〜てほしい — wanting SOMEONE ELSE to do it (行ってほしい). Mixing up 〜たい and 〜てほしい is a very common mistake: 日本に行きたい means I want to go; 日本に行ってほしい means I want someone else to go.
The negative has two forms: 〜ないでほしい (hoping someone won't do something — ゴミを捨てないでほしい) and 〜てほしくない (not wanting someone to do something). Like ほしい and 〜たい, this pattern describes direct emotion, so it's used only for your own wishes; to talk about a third person's wishes, add と言っている or use 〜たがる from the conjecture chapter.
Examples
母にもっと休んでほしいです。
I want my mother to rest more.
友達に早く元気になってほしいです。
I hope my friend gets well soon.
ここにゴミを捨てないでほしいです。
I wish people wouldn't throw trash here.