He was angry that he didn't ask for leave from his superiors on a business trip. what should he do ？

It's better to report this matter to the superior face to face when he comes back. Arguably, there is nothing wrong with you, and you don't need to ask for leave at all, but since the leader is angry, you don't have to find any excuse, just report it truthfully and apologize for doing things well. You can say to your superior: "Leader, I heard that you asked me for something last week? ! I had something to do at home temporarily, and XXX (the superior) asked me for leave, but I didn't say you had other plans at that time. I'm really sorry! I'll pay attention next time! "