{ 5 . 69 - 3. 96 . [  45 + 55  + ( 96^2 - 192 ) : 100 . 50^3 - 40^3 + 35^2 ]  .6 }

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

First, let's simplify the expression inside the parentheses:
96^2 - 192 = 9216 - 192 = 9024

Next, let's simplify the expression inside the brackets:
45 + 55 + 9024 : 100 . 50^3 - 40^3 + 35^2
= 45 + 55 + 9024 : 100 . 125000 - 64000 + 1225
= 45 + 55 + 9024 : 100 . 61000 + 1225
= 45 + 55 + 9024 : 100 . 62225
= 45 + 55 + 90.24 . 62225
= 45 + 55 + 5598.96
= 5698.96

Finally, let's solve the entire expression:
5.69 - 3.96 . 5698.96 . 6
= 5.69 - 3.96 * 5698.96 * 6
= 5.69 - 3.96 * 34193.76
= 5.69 - 135340.0896
= -135334.3996

Therefore, the value of the expression is approximately -135334.3996.