、。
She's asking how such a thing is possible.
Literal
She [topic-は], why that-kind-of thing [subject-が] possible [explanatory-のか] [quotative-と] asking.
An indirect-speech construction. The inner clause どうしてそんなことが可能なのか ('why is such a thing possible') is marked as a question by の+か, then quoted by と and embedded under 尋ねている ('is asking'). 尋ねる is more formal/literary than 聞く. The ~ている form here describes ongoing or repeated action — she is in the process of asking, perhaps repeatedly.