What could be the cause of my engine shutting down when accelerating?

Spark, fuel or compression. That's all that matters. Any check engine lights on? How many miles and when was the last time you changed the fuel filter?

Combination of bad engine mounts and a broken air intake hose? When you step on the gas the engine shifts and opens up the hose creating an air leak before the mass air flow meter causing injector shut-down or reduction. ----Just a random thought. Does it start and idle somewhat normal?