。
She was at a loss as to what she should do.
Literal
She [topic-は] what [object-を] should-do [the-fact-that-ということ] [about-について] way-darkened was.
途方に暮れる ('grow dim with respect to one's path') is a vivid set phrase for being completely at a loss — a deep, disoriented stuckness. 途方 means 'way, course' and 暮れる ('grow dark') gives the figurative image of one's path going dark with no clear direction visible. The embedded question 何をすべきか ('what one should do') is wrapped in ということ to turn it into a noun phrase, which is then taken as the object of について. The whole construction has the careful, slightly bookish feel of psychological description.