Can the 4 ton 14 seer goodman heat pump work with air handler model ASPF426016DA?

While it can work, there are a lot of factors to take into consideration here. The first of which is that this system combo is very likely to have nowhere near 14 SEER efficiency. The air handler itself is the main pain point here; judging from the model, the air handler is roughly around 10 years old and will most likely be experiencing a leak within the next 5-10 years. Another concern (and likely the larger concern) is the potential for abnormally high head pressure while operating in heat pump mode. The coils in older air handler models are significantly smaller than those in modern ones. Since the air handler coil is what the condenser actually uses while operating in heat pump mode, the less coil volume in an older model means that pressure will rapidly rise. This pressure build-up might even exceed the outdoor unit's limits of operation.

To put it simply, we strongly recommend against using an old air handler model with a new heat pump model.

If you have any further questions, please call us and we will be happy to assist you.