。
She turned her gaze toward him.
Literal
She [topic-は] his [genitive-の] direction [toward-に] gaze [object-を] directed.
~の方 (ほう) ('the direction of, the side of') is a set noun for marking general direction toward someone or something — looser than precise prepositions. 視線を向ける is a set phrase for 'direct one's gaze, turn one's eyes (toward).' The に marks the destination of the gaze. Note 方 is a homograph: 方 (ほう) for 'direction/side' here, vs. 方 (かた) for 'person (polite),' vs. 方 (ほう) used in comparisons (このほうがいい). Reading depends on context.