First, we need to simplify the division:

15 - 9 1/3 = 14 2/3

14 2/3 divided by 2/3 = (44/3) / (2/3) = (44/3) * (3/2) = 44/2 = 22

Next, we need to simplify the subtraction:

8 9/20 = 8 9/20

Now, we need to simplify the multiplication:

19 2/3 = 59/3

11 7/9 = 106/9

(59/3) - (106/9) = (177/9) - (106/9) = 71/9

Finally, we need to multiply the result by 9/71:

(71/9) * (9/71) = 1

Therefore, the final answer is 1.