Yuka finished reading an English book for the first time in her life.
Literal
Yuka [topic-は] be-born-[since-て] first-time-[to-に] English-of book [object-を] read-finish-[past-えた].
生まれて初めて ('for the first time since being born, for the first time ever') is a fixed idiomatic phrase for emphasizing a truly first-time experience. Built from 生まれる (be born) + 初めて (for the first time). 読み終える is a compound verb — reading + finishing — in its transitive 終える form. Evocative and memorable.