An engine backfiring upon acceleration can be cause by several things but most commonly the engine backfire is caused by the fuel air mixture being to lean when the when the engine is demanding power.
It can sometimes be caused by low fuel pressure by a fuel pump that is failing or a clogged or partially clogged fuel filter.
Bad spark plugs or bad ignition coils or ignition timing could be off as well which can sometimes cause a backfire when accelerating.
A mechanic could plug in a tester into your vehicle and bring up codes that can tell them what is exactly going wrong with your vehicle.
You could also have a leaky intake manifold gasket that could be causing the lean fuel to air mixture ratio which can cause the engine backfire.