。
He hopes the unpleasant memories will fade away.
Literal
He [topic-は] unpleasant memories [subject-が] disappear thing [object-を] is-wishing.
An interesting nominalization. The clause 嫌な思い出が消える ('the unpleasant memories disappear') is nominalized with こと to become the object of 願う ('wish for, hope'). Note the が inside the relative — when a clause is nominalized, the inner subject takes が, not は. 思い出 is a noun-form of 思い出す ('to recall').