。
She couldn't come because she was too busy.
Literal
She [topic-は] busyness [for-のため] could-not-come.
~のため here is the causal use of [noun]+のため ('because of, due to'), distinct from the purpose use ('for the sake of'). The two are surface-identical but disambiguated by the noun: nouns naming a state (多忙 'busyness,' 病気 'illness') tend to read as causes; nouns naming a goal or beneficiary (子供 'children,' 健康 'health') tend toward purpose. 多忙 itself is a Sino-Japanese compound ('much-busy'), more formal than 忙しい. 来られる is the negative potential 来る ('come') → 来られない ('cannot come').