。
She suddenly burst out laughing.
Literal
She [topic-は] suddenly began-to-laugh.
急に paired with the inceptive ~出す compound is the standard kit for 'suddenly burst into [emotion],' working productively across verbs of involuntary reaction. Where 笑い始める would be a neutral 'started laughing,' 笑い出した carries the suddenness of a chuckle escaping or a guffaw bursting out, often involuntarily. Adding 急に doubles down on the unexpectedness, making the laugh feel especially abrupt — out of nowhere, no warm-up.