Missing on acceleration - 1996 Honda Accord

Check for dirty/stuck IAC

The missing while accelerating is likely due to ignition coils and/or spark plugs going bad. The missing while in park is a normal thing. The car has a rev limiter that will not allow the engine to rev to higher than 3000 RPM while in park.

place a inductive timing light on your spark plug wires one at a time;\while the car is in neutral and, running accelerate the engine
when a miss-fire occurs on the bad spark plug wire you will see a missed flash from the timing light's bulb

Some general thoughts - -
when you try to accelerate, a couple of things happen. The engine shifts sometimes, and you put it under a load unlike when it is idling.
Is it possible a wiring harness or a hose is moving when you accelerate ? Is it possible the fuel pressure or ignition module is not good enough to handle the engine under load ? Is the EGR opening early or something causing a vac leak and a lean fuel mixture ?

this a problem ignition timing. Need to reset to manufacturer specification, They imply you need to make a mayor TUNEUP. Pass the scanner/computer for easy diagnostic and fix it. You can have some faulty ignition coil or PCM or BCM or sensor,distributor etc
see the diagram attached.

What engine does it have in it, if its coil pack over single coils per cylinder. Pull plug wire or coil out of last cylinders on passenger side, these are known for getting water in them that causes a miss in acceleration

Year, make and model of your vehicle would help. If you can check for codes in the engine control module, it would also help in better diagnosing your possible issue and resolve.

What have you done so far as to diagnosis ? Have you checked for any vacuum leaks ? Have you checked if your coils/plugs are in good condition ? Adding as much detail information is best.

Sounds like you have a leaking cylinder head gasket

the idle controls could be the problem

sounds like the mass air flow sensor is malfuntioning