～てほしい

About

The ～てほしい ("I want X to happen/I want someone to do X") combines a て form verb with the い-adjective 欲ほしい. ～てほしい can be used to describe what the speaker wants someone else to do, or what they want to happen, but it can't be used for things that the speaker wants to do themselves.

E.g. これを食たべてほしい。 "I want you to eat this."

E.g. 雨あめが降ふってほしい。 "I want it to rain."

Because ほしい is an い-adjective, it can be further conjugated as well:

E.g. これを食たべてほしかった。 "I wanted you to eat this."

Summary

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  ～て欲ほしい means "I want (someone) to do X" or "I want X to happen"

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  ～て欲ほしい can't be used for things the speaker wants to do themselves