〜てほしい

When you want somebody to do something, you can describe your wish by using the te-form of a verb and the adjective ほしい. The person the wish is directed to is marked with the particle に.

私はびょうきのともだちにげんきになってほしいです。

I want my sick friend to get well.

(私わは)personに verb te-form ほしい    = I want (person) to do...

When you want to say you don't want them to do something, you can negate ほしい and say 〜てほしくありません or negate the verb and say 〜ないでほしいです。