。
She cherishes the precious memories from her childhood.
Literal
She [topic-は] childhood [genitive-の] precious memories [object-を] is-cherishing.
大事にする and 大切にする are near-twins, both meaning 'treasure, value, hold dear.' 大事 leans slightly more practical/important; 大切 slightly more emotional/precious — but they're freely interchangeable in this kind of sentence. The progressive ~ている form locks in 'is currently treasuring,' implying the cherishing is an ongoing state rather than a one-time act. Note 子供のころ ('childhood, the time when one was a child'), where ころ softens the time reference and evokes a stretched-out period rather than a specific moment.