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She's busy studying for exams.
Literal
She [topic-は] exam-study [with-で] busy.
Another use of causal/instrumental で: the activity 試験勉強 ('exam study') is what's keeping her busy — 'busy with X.' The compound noun 試験勉強 stacks two Sino-Japanese morphemes (試験 'exam' + 勉強 'study') into a single unit, a productive Japanese pattern for naming activities. Note that Japanese can package the same situation as either a noun phrase plus で (this sentence) or a verbal clause plus のに ('busy doing X') — two parallel options for the same meaning.