。
She read the letter over and over again.
Literal
She [topic-は] that letter [object-を] many-times many-times re-read.
何度も何度も is reduplicated for emphasis ('many many times,' 'over and over and over') — Japanese loves to double adverbs and mimetics for intensification. 読み返す is a compound verb fusing 読む ('read') + 返す ('return'), meaning 'to reread.' The ~返す suffix is productive: 言い返す ('talk back, retort'), 思い返す ('reconsider'), 取り返す ('take back'), 折り返す ('fold back, turn around'). The picture is of intense, repeated engagement with the letter — perhaps cherishing it, struggling with its content, or trying to extract a hidden meaning.