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She wasn't foolish enough to smoke in front of him.
Literal
She [topic-は] his [genitive-の] front [at-で] cigarette [object-を] smoke [like-ような] foolish [adj-な] thing [contrast-は] didn't-do.
A nicely structured rejection: '(she) didn't do a foolish thing such as smoking in front of him.' ~ような ('like, such as') gives an example of a category — here, 愚かなこと ('foolish thing'). The whole noun phrase acts as the object of しなかった ('didn't do'); the は after こと is contrastive ('such a foolish thing — that, she didn't do'). たばこを吸う ('smoke a cigarette' — literally 'pull tobacco') is the standard idiom for smoking; the verb 吸う ('inhale, draw') applies to anything inhaled (also tea, soup, breath).