To solve this equation, we first need to simplify each individual expression within the parentheses.

1 1/2c - 3/8 = 3/2c - 3/8 = 12/8c - 3/8 = (12c - 3) / 8

1 5/6 - 1 1/3c = 11/6 - 4/3c = 11/6 - 8/6c = (11 - 8c) / 6

Now we can substitute these simplified expressions back into the original equation:

(12c - 3) / 8 - (11 - 8c) / 6

To combine these fractions, we need a common denominator, which in this case is 24.

(12c - 3) / 8 3/3 = (36c - 9) / 24
(11 - 8c) / 6 4/4 = (44 - 32c) / 24

Now the equation looks like this:

(36c - 9) / 24 - (44 - 32c) / 24

Combining the fractions we get:

(36c - 9 - 44 + 32c) / 24
= (68c - 53) / 24

Therefore, the final simplified answer is:

(68c - 53) / 24