The carburettor how to adjust the air and fuel mixture on the carburettor

That sounds like a fuel/air mixture problem.

Just to confirm .. it is a carburettor, not fuel injection?

As a general rule of thumb (with carburettors..) if it backfires through the exhaust/muffler .. the fuel mixture is too rich.

If it backfires through the carb/air filter, the mixture is too weak.

It could also be a 'sticking' float in the carb.

When an engine is cold the fuel is rich .. lots of fuel .. that's how a choke works.. However, when the engine warms up a rich mixture causes problems. The car may splutter and stall, run sluggish or cut out.

the CO and fuel/air mixture is not adjustable on modern cars , only on carburettors . the engine management system will ensure correct fuelling, if there is a fault with this then in most cases an engine management light will illuminate on the dash board

Problem with Cars & Trucks
Air fuel mixture screw adjustment of spaco 17d carburettor Open Question

All internal combustion engines have the same requirements. They must have the correct air fuel mixture and source of ignition in order to run. Although I am unfamiliar with the system you have, the fact thst it will start without the air filter but won't with the air filter indicates that you either have a dirty air filter (you said yours was clean) or you have too much fuel entering the combustion chamber. Beyond that I would only be guessing the reason (air fuel mixture regulator, worn jet, wrong size jet, something else bocking air flow etc.)

The fuel lines may have become air-locked.This can happen if the tank is run dry. If the saw has a primer bulb, alternatively press it several times and then try to pull start the engine with choke on. Repeat this several times. The primer bulb should feel spongy and fill with fuel.
If you're up to it, you can dismantle the carburettor and clean any dirt from valves.The carburettors on chainsaws, hedge cutters etc. are very fiddly with delicate diaphragms, valves and springs so you have to be careful to avoid damage or loosing parts.
Ensure air filter is clean. Foam elements can be washed with hot water and detergent, squeezed dry in a cloth and re-oiled with a teaspoon of engine oil spread through the foam. Paper elements can be cleaned with compressed air blown from the inside of the filter but ideally should be replaced.
Check fuel lines aren't kinked or blocked restricting fuel flow.
Ensure fuel filter isn't dirty. This is probably located at the end of the fuel line in the tank.
Check the throttle cable is actuating the throttle plate in the carburettor.
Check whether there is a vent on the tank or on fuel cap. There is usually a valve on this to allow air into tank to replace fuel as it leaves for the carburettor. Ensure this isn't blocked.

It could be that one of the jets needs replacing but most likely you need to adjust the fuel/air mixture on the carburettor.
It is probably too lean - if you remove the spark plug and have a look at it - is it pale ash grey in colour?

Exactly how you adjust the mixture will depend on the make and type of the carburettor. It's not easy to get it right without expensive workshop test equipment
But there will usually be a small screw with a spring wrapped around it. With the engine running evenly at normal temperature undo the screw slightly by no more than 1 quarter turn at a time until the engine begins to falter then tighten it by one full turn.

Start by cleaning the fuel tank (water from condensation accumulates in it), clean the fuel lines, clean and adjust the carburettor, drain the old oil, remove the sparkplugs,put some fine oil in the cylinders and crank the engine manually, put new oil,oil filter,sparkplugs,distributor cap and air filter, replace the water and start the engine. Check for leaks, run the engine for an hour followed by an oil engine cleaner.

I think maddogcycle is right. One cylinder is running rich and the other running lean. It seems as though they have not been balanced properly and the mixture not accurately adjusted. The settings on these carburettors are critical and must be adjusted with the proper gauges. I'd advise you to have the carbs cleaned and adjusted and tuned to the engine for balance of inducted air flow and fuel/air ratio (mixture)

try sanding the magneto and adjust the fuel air mixture screw till it smooths out

Hey June, the correct assembly. cleaning. setting, and adjustments of the carburetor are CRITICAL....Please take the carb to a qualified professional to get it cleaned and set. Ask him which screw sets the idle speed..and you can set it when you reassemble it.. (ONLY adjust the idle speed screw!!)
IF this machine has oil injection, and its been working fine.. do not adjust it...AND .. if the oil is injected into the carb (i've seen one or two bikes with this set-up)..its working fine..the fuel/air will be taken care of when the carb is fixed! Make sure your air filter is clean!!.. and a new spark plug will help!!