。
She caught the heart of every young person in the neighborhood.
Literal
She [topic-は] neighborhood [genitive-の] all [genitive-の] young-people [genitive-の] heart [object-を] pulled.
心を引く is a set phrase, slightly more poetic than the everyday 引き付ける ('attract, draw to oneself') — 'to pull on someone's heart, capture someone's heart.' 若者 ('young person, youth') is a single word, distinct from 若い人 ('a young person' as a phrase). The triple genitive 近所の・全ての・若者の chains modifiers naturally. 全て ('all, everything') here is the noun-form of 'all,' modifying 若者 attributively via の.