i have a pair of 6x8 infinity speakers in the front and back which are rated at 60 watts. I was looking into getting a 4 channel infinity amp to power them which claims it is putting out 111 watts RMS x 4. Now is this going to blow the speakers?

 

not if you keep the gain down, Its if you run the gain to the point where you you exceed the speakers mechanical powerhandling or thermal handlings. Usually you can hear the mechancial quite easily. Just use the crossover properly and you should get the volume that is desired without damaging them.