。
She gave me a tantalizing look.
Literal
She [topic-は] [troubling-悩ましい] gaze [with-で] me [object-を] looked.
悩ましい is an evocative adjective — 'tantalizing, troubling, vexing.' Originally describing the speaker's own torment ('something that worries me'), in modern usage especially with looks/gazes (目つき) it has shifted to describe an outwardly seductive or stirring quality. 目つきで uses で to mark manner — 'with a (kind of) gaze.'