To estimate the difference between 6 7/8 and 2 1/8, we can round both numbers to the nearest whole number.
6 7/8 is closer to 7 than to 6, and 2 1/8 is closer to 2 than to 3.
So, we can round 6 7/8 up to 7 and 2 1/8 down to 2.
Now we have the simpler problem of subtracting 2 from 7:
7 - 2 = 5
Therefore, the best estimate of the difference between 6 7/8 and 2 1/8 is 5.