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.