。
She couldn't hold back her laughter.
Literal
She [topic-は] laughter [object-を] suppressing [nominalizer-こと] [subject-が] couldn't-do.
笑いを抑える (わらいをおさえる, 'to suppress laughter') uses 抑える ('to suppress, to restrain, to hold back'). The ~ことができなかった is the formal negative-past potential: she was unable to suppress it. The sentence implies a situation where laughter was inappropriate but irresistible.