。
She gave him a sidelong look.
Literal
She [topic-は] him [object-を] sidelong-eye [with-で] looked.
横目で見る is a set phrase meaning 'to look at sidelong / out of the corner of one's eye' — 横目 ('sideways eye') describes both the physical action (eyes turned aside) and the mental attitude (suspicion, dismissal, or covert observation) that often goes with it. The で here is instrumental — the sidelong eye is the means of looking. Implies the look was distrustful or evasive rather than direct.