What's the best way to impress other people?

Pretty much anything other than self-promotion. There's a lot of evidence that when people toot their own horns it tends to backfire. People will judge them as arrogant, narcissistic, and especially as insecure. They know that if you were really amazing you wouldn't have to work so hard to tell other people how amazing you are. Research suggests that instead of promoting yourself it's more effective if other people promote you because after all you're not a credible judge of your own abilities and accomplishments. But if other people think highly of you and they're willing to talk about that that can go a long way. And so, if you're in a situation where you feel like you have to self-promote, then it's worth asking, "OK, over my career, who are the people that I've really impressed?" "Who are not only willing but maybe even excited to sing my praises." And then, "how can I invite them to do that in an honest and genuine way?"