。
She won't admit that she's wrong.
Literal
She [topic-は] herself [subject-が] is-being-wrong fact [object-を] does-not-acknowledge.
The こと-nominalization treats her wrongness as an abstract proposition — a fact in the world to be recognized — rather than something concrete and observed. The こと version reads as slightly more formal and objective; in journalistic or essayistic prose, こと is the default. In speech, a more vivid, concrete framing might prefer の. The semantic difference between the two nominalizers is small, but recognizing this knob is a meaningful step beyond textbook nominalization.