To solve this expression, we follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right):

Convert all mixed numbers to improper fractions:
2 3/5 = 13/5
1 1/2 = 3/2
4 3/5 = 23/5
3 1/2 = 7/2
5 5/6 = 35/6
6 1/2 = 13/2

Perform addition and subtraction within each pair of fractions:
3/5 + 13/2 = 6/10 + 65/10 = 71/10
35/6 + 23/5 = 175/30 + 138/30 = 313/30

Perform addition and subtraction with the results from step 2:
7/2 - 71/10 = 35/10 - 71/10 = -36/10 = -18/5
-18/5 + 313/30 = -108/30 + 1045/30 = 937/30

Multiply the final result by 24:
(937/30) 24 = 937 24 / 30 = 22488 / 30 = 749.6

Therefore, the final result is 749.6.