。
She won't admit she's wrong.
Literal
She [topic-は] herself [subject-が] is-being-wrong [nominalizer-の] [object-を] does-not-acknowledge.
Note the nominalizer の rather than こと here — Japanese has both, and the choice is subtle. The の-nominalization tends to feel more concrete, more tied to a specific event or perception, and a touch more colloquial; こと skews abstract and general. So 間違っているのを認めない frames her wrongness as something almost present and observable (the speaker can see it). Both formulations translate to 'She won't admit she's wrong,' but the flavor differs.