To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS):

First, let's simplify the expression inside the innermost parentheses:
9 - 7 = 2

Now, let's simplify the expression inside the brackets:
7.3^2 = 53.29
24 ÷ 6 = 4

Now, let's substitute the simplified values back into the expression:
107 - { 38 + [ 53.29 - 4 + 2^3] } : 15

Next, let's simplify the expression inside the innermost brackets:
2^3 = 8

Now, let's substitute the simplified value back into the expression:
107 - { 38 + [ 53.29 - 4 + 8] } : 15

Next, let's simplify the expression inside the brackets:
53.29 - 4 + 8 = 57.29

Now, let's substitute the simplified value back into the expression:
107 - { 38 + 57.29 } : 15

Next, let's simplify the expression inside the curly braces:
38 + 57.29 = 95.29

Now, let's substitute the simplified value back into the expression:
107 - 95.29 : 15

Next, let's divide 95.29 by 15:
95.29 ÷ 15 = 6.352666666666667

Now, let's substitute the simplified value back into the expression:
107 - 6.352666666666667

Finally, let's subtract 6.352666666666667 from 107:
107 - 6.352666666666667 = 100.64733333333333

Therefore, the final result is approximately 100.64733333333333.