To solve this problem, we first need to convert all the mixed numbers to improper fractions.

9 1/6 = 9 + 1/6 = 55/6
3 1/9 = 3 + 1/9 = 28/9
1 2/7 = 1 + 2/7 = 9/7

Now we can substitute these values into the expression:

55/6 / 11/24 - 28/9 * 9/7

Step 1: Invert and multiply to divide fractions.
55/6 24/11 - 28/9 9/7

Step 2: Multiply the numerators and denominators.
(55 24) / (6 11) - (28 9) / (9 7)
1320 / 66 - 252 / 63

Step 3: Simplify the fractions.
20 - 4

Step 4: Subtract.
20 - 4 = 16

Therefore, 9 1/6 : 11 / 24 - 3 1 / 9 × 1 2 / 7 = 16.