Several Causes an Engine to Backfire Through the Exhaust but depending on the conditions.
Reasons what causes an engine to backfire through the exhaust
(1) Air injection system problem
(2) Valve not sealing.
(3) Engine timing is off.
Car Troubleshooting
If backfiring only occurs when decelerating or slowing down, this suggests a possible problem with the air injection system.As indicated above, backfiring only occurs when decelerating. This points to a possible problem with an emissions control device known as the "air injection system". In particular, the air injection system's diverter valve has most likely failed. Let's elaborate on this a little.
An air injection system basically works by pumping fresh air into the exhaust manifold. This causes any unburned gases to burn before going out of the tailpipe and into the atmosphere.
Now, when a vehicle is decelerating, the air/fuel mixture is very rich. This means a lot of unburned gases will be in the exhaust manifold. If these unburned gases are exposed to fresh air, a mini-explosion (i.e. backfire) will occur. Thus, it's the job of the diverter valve to divert the flow of fresh air away from the exhaust manifold during deceleration. Clearly then, if the diverter valve is bad, the engine will probably backfire when the vehicle is decelerating.
What to do?
First, take this vehicle to a garage and ask the mechanic to check the air injection system, in particular, its diverter valve. Explain the situation to the mechanic exactly as you read and explained it to you by this article. It's very important to demonstrate some knowledge about the problem to the mechanic.
Now, as was discussed in the explanation for this diagnosis, the most likely culprit is a bad diverter valve. However, it is still possible that something else is causing this vehicle to backfire. Unfortunately, it's simply impossible to know with 100% certainty without actually inspecting the vehicle. With that said, get several opinions from various repair shops and then make a decision based on all the information.
If backfiring does not occur when decelerating or slowing down, this suggests a problem of a valve not sealing and or engine timing is off.
Since backfiring only occurs while decelerating, from this, we made the assumption that the engine is probably backfiring under a wide variety of circumstances. Therefore, the cause is probably a valve and/or timing related. Let's look at each possibility.
"Valves Not Sealing" - If the valves aren't sealing well, some fuel may leak into the exhaust manifold. If the manifold is reasonably hot, this leaked fuel will ignite (i.e. backfire) and the sound will be heard through the tailpipe.
"Engine Timing Off" - If the timing is off, the spark from each spark plug will occur when a valve is partially open. This can cause the combustion of the air/fuel mixture to partly occur in the exhaust manifold (i.e. backfire) and the sound will thus be heard through the tailpipe.
What to do?
Take this vehicle to a garage and have the mechanic check the valves and timing. The valves could be burned or simply out of adjustment. Timing problems are generally caused by a worn/slipping timing belt or chain. When looking for a garage, try to find one that's approved by the AAA. Such garages are reputable and, best of all, if you do have any kind of dispute after the work is done, the AAA has the policy to investigate the situation and resolve it.