The girl went. away---

The correct choice in this case is "laughing." This is because the word "laughing" is used as a present participle, which describes an action happening at the same time as the main verb ("went"). In this sentence, it suggests that the girl went away while she was laughing. The other options do not fit grammatically or logically in the sentence. "Laughingly" is an adverb that would describe how the girl went away, but it does not match the verb form. "Being laughed" is a passive construction that does not make sense in this context. "With laugh" is grammatically incorrect, and it should be "with laughter" if it were a valid option.