driving 2 12v 2A DC motors with Mega

1.8 Ohms sounds reasonable, in which case the start/stall current, operating from a 12V supply, would be around 6.7 Amps. A 10 Amp motor driver should work.

Or, follow this tutorial for a MOSFET driver http://bildr.org/2012/03/rfp30n06le-arduino/

Contrary to the advice given in that tutorial, you should use a logic level MOSFET, like the one recommended.