To add the fractions and the mixed numbers together, we need to find a common denominator.

1/3 + 1/8 + (-2 1/3 + 3 7/8) - 6 11/12

First, let's convert the mixed numbers to improper fractions:

-2 1/3 = -7/3
3 7/8 = 31/8

Now, find a common denominator for the fractions and mixed numbers:

1/3 = 8/24
1/8 = 3/24
-7/3 = -56/24
31/8 = 155/24

Therefore, the expression becomes:

8/24 + 3/24 + (-56/24 + 155/24) - 6 11/12

Combined:

11/24 + 99/24 - 6 11/12

Now, combine:

11/24 + 99/24 = 110/24 = 55/12

So, the final result is:

-6 11/12 + 55/12

To subtract the fractions, we need to find a common denominator, which is 12:

-6 11/12 = -6 * 12 + 11 = -72 + 11 = -61

Therefore, the final solution is:

-61 + 55/12 = -61 + 4 7/12 = -57 7/12