*don't get in the habit of writing "u". Even informally I don't write it like that. *Did the people say it wrong in the video? Both are ok. Slightly different emphases between the two, but in practice they're essentially used the same. Essentially, whichever pronoun is said first is the person that you want your friend to introduce to the other person. For example "introduce me to your friend" "excuse me (other person), I'd like to introduce to you my friend (your name)" on the other hand "introduce your friend to me" "excuse me (other person), have you had a chance to meet (your name)" They're almost identical, but there's a slight difference in the way people are presented. In a professional setting, the first one is more likely to occur when you're younger than the person you want to meet and second one is when you're older than the person you want to meet. No one will get offended though if it's done the other way around.

你好， Would u introduce me to your friend？ 意思大概是，你朋友是否愿意介绍你给他朋友？ 至于 Would u introduce your friend to me? 意思是， 你是否愿意介绍你朋友给我？ 希望没错吧~