To simplify the expression, we need to perform the operations step by step following the order of operations (parentheses, multiplication and division, addition and subtraction).

First, let's simplify the terms within the parentheses:
3 3/5 = 18/5
1 7/9 = 16/9

Now we can subtract 18/5 by 16/9:
18/5 - 16/9 = (162/45) - (80/45) = 82/45

Next, let's simplify the denominator:
1/2 - 1/3 = (3/6) - (2/6) = 1/6

Now we can divide (82/45) by (1/6):
(82/45) ÷ (1/6) = (82/45) * (6/1) = 492/45 = 10 42/45

Finally, we subtract the result from 24:
24 - 10 42/45 = 24 - (10 + 42/45) = 24 - 10 - 42/45 = 14 - 42/45

Therefore, the final simplified expression is 14 - 42/45.