Would a 20 amp 240 volt panel from the main panel be enough for a laundry room?
If the laundry room does not have an electric clothes dryer, then yes, 20 amps at 240 volts should be adequate.  That could be arranged as a pair of 20 amp 120 volt circuits:  one for the clothes washer and an iron, and the other for the motor of a gas or propane clothes dryer.

However, if an electric clothes dryer is needed, that alone should be a 30 amp (or larger) 240 volt dedicated circuit.  Another 120 volt circuit at 20 amps for the clothes washer and iron, etc.  The total is at least 50 amps.