N4
ように～てほしい
Want ~ to ~ like ~, Want ~ to be able to ~, Want ~ to ~ in the way of ~
弁護士になれるように頑張ってほしい。
I want you to work your hardest, so that you can become a lawyer.
Explanation
「ように〜てほしい」 means 'I want you to be able to …'. It sounds gentler than a direct demand and carries hope: 「早く一人でできるように、頑張ってほしい」 (I hope you'll do your best to manage on your own soon). Before 「ように」 you usually find a potential form, a verb outside one's will, or a negative. After a noun use 「のように」.
Mixed up with
The person you want to act is marked with 「に」: 「子供に勉強してほしい」 (I want my child to study).
Before 「ように」 comes a potential, non-volitional or negative verb (the aim); the 「〜てほしい」 part is what you wish of the other person.