if the air filter were clogged, it would make the fuel mixture too rich. His issue is the opposite, the mixture is too lean. Although not directly related, I had a set external metering jet unscrew and fall off an edger carb. It only ran when I choked it because of the air leak it caused. I would look closely at the carb, hoses etc., to be sure nothing is missing. That said, if choking the engine by putting their hand over the carb makes it run, then the problem is too lean a mixture, the goal has to be finding the cause of that. It can include bad fuel hose, filter, some defect in the carb, defect in a fuel pump if there is one, cracked manifold, loose manifold, crack in a head, blown head gasket, etc.. Anything that can affect the air to fuel ratio by either letting in too much air or too little fuel. Just choking the carb can cause enough vacuum to pull lots of fuel in. That compensates for not enough fuel or too much air. I do it all the time when running my leaf blower dry of fuel. I drain the tank and it runs off the fumes in the tank, fuel in the hose, and crankcase for about a minute. Then it starts to stumble as it runs out of fuel so I choke it, and it runs another 30 seconds or so because I am artificially affecting the air to fuel mixture. A hand over the carb makes the mixture richer.