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She likes quiet music — baroque music, for example.
Literal
She [topic-は] quiet music [object-を] prefers — for-example baroque music [object-を].
好む (このむ) means 'to prefer' or 'to like' — more literary and deliberate than 好き, suggesting a refined or considered preference. 例えば (たとえば) introduces a specific example: 'for example.' バロック音楽 (baroque music) as the example adds character — this isn't just 'quiet music' but a specific, cultured taste. The dash (ー) before 例えば functions like an em-dash in English, setting off the afterthought.