。
She didn't know how to handle the issue.
Literal
She [topic-は] that issue [object-を] how handle [should-question-べきか] didn't-understand.
~べき is the bookish auxiliary 'should, ought to,' carrying the -き ending of a classical attributive form (it descends from classical Japanese ~べし). Embedded inside an indirect question with か, it gives べきか — 'should one X?' as a question. The whole clause どう扱うべきか ('how she should handle it') becomes the object of わからなかった. 扱う ('handle, deal with, treat') is a versatile verb covering objects, problems, customers, even data — anything that calls for management.