。
She's recovered enough to wash her own hair now.
Literal
She [topic-は] now [as for-では] herself [by-で] hair [object-を] can-wash [extent-ほど] well became.
The pattern [verb potential]+ほど＋元気になる ('became well to the extent that one can do X') uses ほど as a degree marker — 'to the level of being able to wash her own hair.' That detail is the kind of small, telling milestone that signals genuine recovery from illness. 自分で ('by oneself, on one's own') uses で in its instrumental sense: 'by means of self.' 洗える is the potential of 洗う ('wash'), with the typical godan-verb potential ending -える. 今では layers 今 with the topic-marking では, framing the present as a contrast with an earlier, weaker state.