I have a 4 cycle 6hp briggs&stratton lawn tractor. It cranks and fire up. It will run for about 20 minutes and cut off. It will not start back up. Could it be the coil going bad?

Hi,
Could easily be the coil since it uses one coil to fire both cylinders, it is under extra stress. Part #394891 and parts breakdown at:
http://bsintek.basco.com/BriggsDocumentDisplay/Z6ltuBVJ1DajI.pdf
Peace,
Clarke