。
She turned her eyes toward him.
Literal
She [topic-は] his [genitive-の] direction [to-に] eye [object-を] turned.
Compare with 視線を向ける ('direct one's gaze'): same structure, but 目 ('eyes') is the more concrete physical word, 視線 ('gaze, line of sight') the more abstract conscious-attention word. Here the simple 目を向ける is the everyday phrasing. のほう (with hiragana) instead of の方 (with kanji) is just a stylistic choice — both read ほう and mean 'direction.'