// For embed link:

var url = @"https://www.youtube.com/watch?v=6QlW4m9xVZY";

var uri = new Uri(url);

// you can check host here => uri.Host <= "www.youtube.com"

var query = HttpUtility.ParseQueryString(uri.Query);

var videoId = query["v"];

// videoId = 6QlW4m9xVZY 

// For youtube/watch link:

var url = "http://youtu.be/AAAAAAAAA09";

var uri = new Uri(url);

var videoid = uri.Segments.Last(); // AAAAAAAAA09