The problem is to evaluate the expression $4\{100 - [3^2 - 2(10-6)]\}$. We need to follow the order of operations (PEMDAS/BODMAS) to simplify the expression.

1. Problem Description

The problem is to evaluate the expression $4\{100 - [3^2 - 2(10-6)]\}$. We need to follow the order of operations (PEMDAS/BODMAS) to simplify the expression.

2. Solution Steps

First, we simplify the innermost parentheses:

$10 - 6 = 4$

Next, we substitute this result back into the expression:

$4\{100 - [3^2 - 2(4)]\}$

Now, we simplify the exponent:

$3^2 = 9$

Substitute back into the expression:

$4\{100 - [9 - 2(4)]\}$

Then, we perform the multiplication inside the brackets:

$2(4) = 8$

Substitute back into the expression:

$4\{100 - [9 - 8]\}$

Next, we simplify the expression inside the brackets:

$9 - 8 = 1$

Substitute back into the expression:

$4\{100 - 1\}$

Now, we simplify the expression inside the curly braces:

$100 - 1 = 99$

Finally, we perform the multiplication:

$4 \times 99 = 396$

3. Final Answer

396