My little sister hates to (do,doing) your English homework but she’s getting better

Correct choice: My little sister hates doing your English homework, but she’s getting better at it.

Why: After hate, both the infinitive (to do) and the gerund (doing) are possible, but “hates doing” sounds more natural when talking about the activity itself, and “getting better at it” completes the idea clearly. If you keep the infinitive, you’d also usually add “at it” (getting better at it). Example alternatives:

• My little sister hates to do your English homework, but she’s getting better at it.
• My little sister hates doing your English homework, but she’s getting better at it.