。
She seemed to love music.
Literal
She [topic-は] music [subject-が] really-like [seems-なように見えた].
大好き ('to really like, to love') is the intensified form of 好き; the 大 ('big') prefix turns a neutral preference into strong fondness. Combining it with ~ように見えた ('seemed to be like') hedges the assertion: not 'she loves music,' but 'she gave the impression of loving music.' Note how ように takes な before the i-ish-looking 大好き — that's because 好き is a na-adjective despite its appearance.