。
She didn't take my advice gladly.
Literal
She [topic-は] my advice [object-を] gladly didn't-receive.
快く is the adverbial form of the i-adjective 快い ('pleasant, delightful, agreeable') — a fairly literary word that survives in modern Japanese mostly in stock adverbial uses like 快く引き受ける ('agree willingly') and 快く受ける ('accept gladly'). The negation 受けなかった here turns the whole expression into 'didn't accept gladly' — i.e., received it grudgingly or with resentment. 忠告を受ける is the standard collocation for 'taking advice,' with 受ける in its 'receive, accept' sense.