What is an estimate of 5 1/8 * 6 5/6?

Well estimating is just rounding to the nearest whole (in this case, because you don't specify). So what you just get it 5*6. Remember the rule for rounding is anything half or above rounds up, anything below half rounds down. Same with all the digits.

First change to improper:

5 1/8=41/8

6 5/6=41/6

41/6 (41/8)

=1681/48

35 1/48