They're both grammatically correct, but the first one is the more common and natural way of saying it. By the way, the name of the genre in English is "K-Pop."

The first one shows that you are unsure - you think he doesn't like it but you're not sure why you think it. The second one sounds more certain. Rather than just not knowing, you actively think it's true. Maybe you have some evidence to back it up.

They are both correct. I prefer the second one. It is more clear. I am a native English speaker and teach using clear and simple language. I hope that helps.

Both sentences are grammatically correct, but they are used in slightly different contexts: 1. "I don't think that Tom likes K-music." – This is more commonly used and sounds more natural in conversation. It implies you doubt or are unsure whether Tom likes K-music. 2. "I think that Tom doesn't like K-music." – This is also correct but emphasizes that you're more certain that Tom dislikes K-music. Both are acceptable, but the first is more commonly used.