How do you clean the carburetor on a 2002 Honda vlx 600?

Although I cannot be specific with this make and model, this trick has worked on numerous vehicles over the years. Disconnect the fuel line and unscrew the drain plug, which is located on the side or bottom of the carburetor bowl. Drain as much gas out as possible. Also drain and clean the fuel strainer and clean it with carburetor cleaner. Now either spray or pour carburetor cleaner into the fuel line and let it drain through the carburetor. At first it may not drain, but as it removes the varnish and gunk it should soon begin to flow. For really stubborn and a through cleaning of the carburetor you can replace the plug and fill the fuel line with cleaner and let it sit.

I've done this in chainsaws, boats, bikes and cars over the years and have always fixed the problem.