。
She was completely at a loss for what to do.
Literal
She [topic-は] [what to do-どうして良いか] at-a-loss-fell.
途方に暮れる is a vivid set phrase for being utterly at a loss — literally 'to be benighted on a way / to fall into evening on a path.' The image is of a traveler caught out at dusk with no idea which road to take. 途方 ('way, course') by itself is rarely used outside this idiom. The lead-in どうして良いか is itself a fixed embedded question 'how (one) should act,' with良い (or いい) standing in for 'good / right / appropriate to do.' The combination is the standard high-frequency way to express 'didn't know what to do' in slightly elevated register.