。
She doesn't like going out.
Literal
She [topic-は] going-out-disliking is.
外出嫌い is a compound noun: 外出 ('going out') + 嫌い ('disliked'). Japanese productively builds these noun-嫌い compounds for personality descriptions: 人嫌い ('misanthropic'), 勉強嫌い ('study-averse'), 野菜嫌い ('vegetable-hating'). 嫌い grammatically behaves as a na-adjective in this slot, so the predicate is 外出嫌いだ. The pattern lets you bake a behavioral preference into a single label, which Japanese often prefers over expanded clauses ('she dislikes going out' → 'she's a going-out-disliker'). The bare だ closes the sentence in plain casual form.