。
She couldn't bring herself to look at his face.
Literal
She [topic-は] his [genitive-の] face [object-を] see thing [subject-が] could-not.
~ことができる/できない is the periphrastic potential — 'can/cannot do.' Slightly more formal and explicit than the inflectional potential (見られる/見られない). The の inside the embedded 見ること clause acts like の/が in a subject role within a nominalized clause. The whole phrasing has a slightly ceremonial air, often used when the inability is emotionally or socially weighted (couldn't bring oneself to do).