To solve the expression 3/8 * (5/9 - 1/6), we first need to simplify the operation inside the parentheses.

5/9 - 1/6 can be rewritten with a common denominator:

5/9 - 1/6 = (52)/(92) - 1/6
= 10/18 - 3/18
= 7/18

Now, we substitute this value back into the original expression:

3/8 * (7/18)

To multiply fractions, we simply multiply the numerators together and the denominators together:

= (3 7) / (8 18)
= 21 / 144

Therefore, 3/8 * (5/9 - 1/6) is equal to 21/144, which can be simplified further to 7/48.