Maybe, maybe not?
Assuming you mean the 6mm Remington and not some other 6mm… the case head size on the 6mm is 0.472"
The case head size on the .308 is 0.473" That's a nominal difference and the stock bolt face might work just fine. If not it wouldn't be much work for a gunsmith capable of doing the rebarrel job to open it up.
Don't know what might need to be done to the magazine to make it feed right.