Let's solve this step by step:

First, we need to calculate 2 5/12 * 11/18:

Convert 2 5/12 to an improper fraction:
2 5/12 = (2*12 + 5)/12 = 29/12

Now, multiply 29/12 by 11/18:
(29/12) (11/18) = (2911) / (12*18) = 319 / 216

Next, subtract 1/6 from the result of the previous calculation:

319 / 216 - 1/6 = (319/216) - (36/216) = 283/216

Therefore, the answer is 283/216.