What makes a two stroke engine produce twice as much power as a four stroke?

A 2-stroke engine makes power every2 cycles were a 4-stroke makes power every 4.Hence 2x power.

This is absolutely INCORRECT! A two stroke engine develops it's PEAK horse power twice as fast as a four stroke for the reason given but that is it. For a given displacement a four stroke engine will ALWAYS make more torque and horsepower than a two stroke engine of equal displacement. This is due to the fact that a four stroke engine cleans the cylinder of contaminated (exhaust) air, compresses the air/fuel to a more efficient level, and draws a cleaner air/fuel mixture into the cylinder as there is no slow burning, air/fuel mixture contaminating oil mixed in the combustion charge. I have over forty years experience working on engines, and can tell you, the ONLY reason two stroke engines have lasted this long, is due to the fact that they weigh less than an equivalent horsepower four stroke engine. If they DID develop more horsepower, the four stroke would not have become the standard internal combustion engine used in transportation, generators, air compressors and the like.