。
She accepted his offer.
Literal
She [topic-は] his [genitive-の] offer [object-を] accepted.
受け入れる is a 複合動詞 combining 受ける ('receive') + 入れる ('put in') — 'take in, accept, welcome (into one's circle/decision).' Used both for accepting offers, proposals, or applications, and for accepting people into a group. 申し出 ('offer, proposal') is the noun form of 申し出る ('to propose, offer'); 申す is a humble form of 言う, so 申し出る carries a slight humble nuance — 'to humbly bring forward (an offer).'