。
She can't control her emotions.
Literal
She [topic-は] her own emotions [object-を] suppress thing-が able-not.
感情を抑える ('to control / suppress / hold back emotions') is a standard collocation. 抑える ('to press down, hold back, restrain') applies physically (押さえる is the more concrete cousin) and metaphorically (controlling impulses, anger, tears). ~事ができない is the formal potential negation pattern; 事 is written here in kanji rather than the more common kana こと. The construction describes a chronic state — she can't reliably keep her emotions in check.