The question, “What does Sue's cat like?” does not sound very natural. This is because it feels incomplete. The person hearing the question would wonder, “like what?” Better sentences: What does Sue's cat like to play with? What does Sue's cat like to eat? What does Sue's cat like to do while she is awake? *I would like to mention with the first sentence, in formal English you cannot end a sentence with the word “with.” The grammatically correct sentence would be, “With what does Sue's cat like to play?” However, that type of formal English is not common in spoken English. Spoken causal English would use the example I wrote above. I hope this helps. :) If you would like to practice speaking, please feel free to look at my teaching profile and class offerings. Kristin https://www.italki.com/kagcafe

What are you trying to say?

yeah , it's right