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She does what her parents tell her.
Literal
She [topic-は] parents [possessive-の] say things [object-を] well listens.
言う事を聞く (いうことをきく) is a set phrase meaning 'to do as told, to obey.' Literally 'to listen to the things (someone) says,' but in practice it means compliance rather than just hearing. 良く (よく) here means 'well, properly' — she obeys reliably. This phrase is particularly common in parent-child contexts.