Use synthetic division.  In order for x - 2 to be a factor of the original polynomial,
synthetic division with a divisor of 2 must have 0 as a remainder:

2  |  3   -m       -6         8
   |       6       12 - 2m   -8
   ============================
      3    6 - m    6 - 2m    0

So the result of multiplying 2 times 6 - 2m must be -8


Solve 12 - 4m = -8 for m.