I want to start by saying that to my eye, this looks like a perfectly fine backed-up answer. If I saw it in the queue, I'd flag at is "Lookin' alright." That being said, if you really want to get nitpicky, I see a couple things here that you could change to make this a better answer...
Reading your answer pre-edit (the big bold "Note:"), I see the following:
I have had this kind of friend that [...]
Oh nice! You've been through this kind of situation before, so your answer will probably come from a place of experience. I like it.
I would start with something really simple, [...]
The first thing I would do is [...]
This should [...]
Then you could [...]
Okay...this is looking like a whole lot of "Do this!" without really any explanation of why this is the right choice. You opened with telling us you've been in this situation, so I can guess this is from experience. But what I'm really interested in is why your experience led you to thinking this is the right answer. What's the thought process behind this? You say "He should [act this way]" or "This should [have this outcome]" but what makes you think that?
And then we get to the very end:
I have a friend that has this kind of extreme view and he doesn't hear anything other people has to say, he knows better. I have watched how he has damaged many of his relationships with other friends. I tried this technique I told you and it didn't work out. He was just too extreme.
Wait, so the advice you just gave didn't work for you? What makes you think it'll work in this situation then? Is it because OP's friend is less "extreme?" What led you to that conclusion?
Your edit answers a lot of that last question by giving us more insight into what happened when you did this with your friend and how that outcome may benefit the OP, but the biggest place this answer can benefit is in the middle with all those "Do this!" parts.
There's nothing wrong with giving all your advice up front and your experience and reasoning at the end. Like I opened with, your answer already looks perfectly fine to me. But the best answers I've seen on this site manage to interweave their reasoning and experience into their advice, which gives it even more impact.
This doesn't mean you have to "disclose more information on what you did with names1 and sentences." You don't need to give a full retelling of the event--and in fact, that may even hurt your answer as it'll draw away from the advice you're actually trying to give. Rather, we just want to know why you think your answer will work. Where is your advice coming from? And from your latest edit, it sounds like there are other situations and other friends' experiences that you can draw from.
1. Please never feel required to give names on this site! A person's name adds absolutely 0 information to the post except as something to identify that character by. Don't be afraid to have fun with it ;) https://www.name-generator.org.uk/quick/