To Begin To Blow, To Spout Out, To Burst Out Laughing
intransitive verb, godan verb
If 吹く is "to blow" and 出す is "to remove," then you are removing your blowing. You need to begin to blow to do that!
ふきだす
The readings come from 吹く and 出す.
俺の新しい髪型を見て、あいつプッと吹き出したんだぜ。失礼だよな。
She chuckled when she saw my new hairstyle. That’s rude, isn’t it?