Questions & Answers about Я люблю слушать музыку у него дома.
Музыку is in the accusative case, because it is the direct object of the verb слушать (to listen to).
In Russian:
- Nominative (dictionary form): музыка – used for the subject of the sentence.
- e.g. Музыка громкая. – The music is loud.
- Accusative (direct object): музыку – used after verbs like слушать, любить, слышать, etc.
- e.g. Я слушаю музыку. – I am listening to music.
So in слушать музыку, "music" is what you are listening to, so it must be in the accusative: музыку.