Most efficient way to step down 48V to 12V high amperage
The most efficient way to create a lower voltage at higher current from a higher voltage at lower current is a type of switching power supply called a buck converter.  For a buck converter, (watts out) = (watts in) - losses.  For a linear regulator (current out) = (current in) - losses.

Buck converters up to 85% or so efficient are relatively easy to make yourself.  You have to wake up and take it seriously to get over 90%.  Getting 95% requires someone that knows what they are doing really applying themselves to the problem.

There is much written about buck converters out there, and the term "buck converter" should be a useful search term.  Therefore I'll only explain the general concept briefly.



When the switch is closed, current builds up in the inductor.  When the switch is opened, the instantaneous inductor current must continue to flow.  D1 provides a path for this current.  Since the voltage accross the inductor is now negative, the current in it decreases.  The switch opens and closes rapidly to add current to the inductor when closed and causes the inductor current to ramp down when open.  The fraction of the time the switch is closed regulates the overall output current.  This fraction is usually modulated by a feedback loop to regulate the output voltage.

Due to the current path thru D1, the output current is higher than the input current.  If all the components are ideal, no power can be dissipated, and all input power is transferred to the output.