Because she didn't pay enough attention, she can't possibly pass the exam.
Literal
She [topic-は] attention [subject-が] was-insufficient [because-から], exam [on-には] absolutely pass-can-not.
とうてい~ない ('absolutely cannot / can't possibly') is an emphatic negative pattern — とうてい (到底) strengthens the impossibility. 注意が足りなかった ('attention was insufficient') identifies the cause. 合格できない uses the potential form of 合格する in the negative. The には after 試験 adds contrastive emphasis — 'as for the exam (in particular), there's no way.'