Hello, I'm Jina.
취향이 뭐예요 is "what is your style/taste?"
If they are talking about movie, the answer can be 저는 코미디 좋아해요 / 제 취향은 코미디 영화예요 ( Comedy movies are my cut of tea )
If they are talking about coffee, the answrt can be 저는 라떼 좋아해요 / 제 취향은 라떼예요.
I hope it will help you :)