She could no longer stand his rude words.

Literal

She [topic-は] his [genitive-の] rude [adj-な] words [at-に] already couldn't-endure-anymore.

A nice morphological stack on the verb: 我慢できる ('can endure') → 我慢できない ('can't endure') → 我慢できなくなる ('come to be unable to endure') → 我慢できなくなった ('came to be unable to endure'). The ~なくなる construction marks a transition into a state of inability — 'started being unable to.' Pairing this with もう ('already, anymore') strengthens the breaking-point feeling: she crossed a threshold from 'tolerating' to 'no longer tolerating.'