To evaluate the expression \( 32 - (4 + 2 \times 3) \times 2 \), we will follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right).
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Start with the expression inside the parentheses: \( 4 + 2 \times 3 \).
- First, we perform the multiplication: \[ 2 \times 3 = 6 \]
- Now substitute back into the parentheses: \[ 4 + 6 = 10 \]
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Now substitute this result back into the original expression: \[ 32 - (10) \times 2 \]
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Next, perform the multiplication: \[ 10 \times 2 = 20 \]
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Now substitute this result back into the expression: \[ 32 - 20 \]
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Finally, perform the subtraction: \[ 32 - 20 = 12 \]
Therefore, the value of the expression is \( \boxed{12} \).