Always remember the equation:

Volts x Amps = Watts

So charging a 4s pack at 20 amps is roughly 360 watts (16v x 20a = 360w). Watts going out must equal watts coming in plus around 10% extra for charger in-efficiency. Not worrying about the charger in-efficiency, a 12v power supply would need to put out around 30 amps. While a 24v power supply would need to put out only 15 amps.

Try to charge two 4s packs at 20 amps with your 12v power supply and you are getting pretty close to it's limit. Also, higher amps going into a charger is harder on the charger than lower amps.