。
She turned down my proposal.
Literal
She [topic-は] my proposal [object-を] refused.
申し込み ('application, request, proposal, formal offer') is a parallel derived noun to 申し出 — same source verb 申し込む ('to apply for, propose'), nominalized via the masu-stem. The two overlap heavily but split slightly: 申し出 leans toward voluntary offers (offering help, offering to do something), while 申し込み leans toward applications and formal proposals (applying for a job, proposing marriage). In a romantic context, 結婚の申し込み ('marriage proposal') is the standard term.