。
She suddenly burst into tears on hearing the news.
Literal
She [topic-は] that news [object-を] hearing [then-て] suddenly burst-out-crying.
突然 ('suddenly, abruptly') is a formal-leaning sino-Japanese adverb, more clipped and dramatic than 急に ('suddenly') in casual speech. 泣き出す is a compound verb 'cry-burst-out' (from 泣く + 出す), capturing the eruptive quality of a sudden cry. The te-form 聞いて chains hearing to crying: the news arrived and the tears immediately followed. Notably, 泣き出す itself doesn't tell you whether the tears come from grief or happiness — Japanese leans on context to disambiguate, and the same verb covers both.