She couldn't hold back her emotions.

Literal

She [topic-は] emotions [object-を] suppress [thing-こと] [subject-が] could-not.

抑える ('to suppress / hold down') is the standard verb for keeping emotions, urges, or impulses in check — same verb used for putting down a rebellion or pressing a button. The pattern Verb + ことができない ('cannot do Verb') is the classic compound potential, more explicit than the conjugational potential 抑えられない and felt as slightly heavier or more deliberate. The construction nominalizes the verb with こと and treats the inability as a missing capacity: literally 'the act of suppressing [her emotions] could not happen.' Emotional restraint (感情を抑える) is a recurring theme in Japanese narrative and moral discourse, where holding feelings in is often valorized.