。
She gladly accepted his proposal.
Literal
She [topic-は] gladly his proposal [object-を] accepted.
喜んで is the te-form of 喜ぶ ('to rejoice') used adverbially: 'with joy, gladly.' It's the standard 'gladly' modifier in Japanese, frequently appearing in service phrases like 喜んでお手伝いします ('I'd be happy to help'). プロポーズ is a katakana loanword that has become the default term for a marriage proposal — the native Japanese equivalent 求婚 ('seeking marriage') exists but feels archaic. The English-derived loanword carries a slightly Western, romantic-comedy connotation.