While your car is decelerating or being slowing down the engine backfires.
Car Problem Diagnosis
When a car backfires during deceleration it only indicates that there is a possible problem on the emission control device which known as the air injection system. Usually the problem on air injection system is that the air injection diverter is failing. The air injection system is the one that pumps fresh air into the exhaust manifold. The purpose of pumping fresh air is to burn any unburned gasses before it gets out the tail pipe.
During deceleration your car air/fuel mixture is rich and a lot of unburned gasses come into the exhaust manifold. If all of these unburned gasses are exposed to fresh air a mini explosion will happened. Now, the diverter valve is the one that diverts the fresh air away form the exhaust manifold when your car decelerate, if the diverter valve is failing the car engine backfire.
Possible Cause of Engine Backfire When Decelerating
Problem with the air injection system
All About Auto Recommendation
Bring your car to a reputable auto repair shop and ask the mechanic to inspect your car air injection system to confirm the problem of the diverter valve. Diverter valve is only a possible cause of the problem. There might be other cause which can only be determined by actual inspection of your car. However before proceeding with the repair seek first for a second opinion of another mechanic before you decide in any repair works.