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To simplify the expression \( (-4) 2 - 32 \div (12 - 4) \), let's break it down step by step. 1. First, calculate the expression inside the parentheses: \[ 12 - 4 = 8 \] 2. Now, substitute that back into the expression: \[ (-4) 2 - 32 \div 8 \] 3. Next, perform the division: \[ 32 \div 8 = 4 \] 4. Now, substitute the division result back into the expression: \[ (-4) 2 - 4 \] 5. Next, perform the multiplication: \[ (-4) 2 = -8 \] 6. Now, substitute this result back: \[ -8 - 4 \] 7. Finally, perform the subtraction: \[ -8 - 4 = -12 \] So, the simplified expression is: \[ \boxed{-12} \]