My grandparents 1992 Honda fourtrax 300 carburetor went bad. It is $370 for a brand new Honda brand one on ebay(the are plug and play. they are adjusted from factory), but the four wheeler was not worth sticking that kind of money into it, so we sold it. My 2008 honda rancher with fuel injection has only had one problem. It would go into de-rate mode. I installed a brand new $135 electric fuel pump and that fixed it. It's been running great for the last 8 years.

Next time take the air filter out first and it will come out a lot easier with the filter and cover removed from airbox.

I imagine you put fresh gas in it? Did you figure out what the issue is? It’s gotta be something minor….check the Honda forums, that helped me lots.