To solve this expression, we first need to convert the mixed numbers to improper fractions:

2 1\6 = 13/6
3 3\8 = 27/8
-3 3\4 = -15/4

Therefore, the expression becomes:

(13/6 - 27/8) * 24 + 1/18 : (-15/4)

Now, calculate the subtraction in the parentheses first:

(13/6 - 27/8) = (104/48 - 162/48) = -58/48 = -29/24

Now, substitute the result back into the expression:

(-29/24) * 24 + 1/18 : (-15/4)

Now simplify the expression further:

(-29/24) 24 = -29
1/18 : (-15/4) = 1/18 (-4/15) = -4/270

Therefore, the final answer is:

-29 - 4/270 = -29 4/270 = -29 2/135