。
She came to like that house.
Literal
She [topic-は] that house [subject-が] like became.
~が好きになる ('to come to like X') uses become-verb なる to mark a change of state — she wasn't a fan before but is now. The が is the same が that pairs with 好き ('liked') in the basic XはYが好き frame; な-adjective stems precede になる to express becoming-that-state. Japanese consistently uses になる for transitions, where English might use 'become', 'come to', 'grow to', or just a simple verb. The pattern works equally for 嫌いになる ('come to dislike'), 好きになる ('come to like'), 上手になる ('become skilled').