To simplify the expression \( 36 - 2 \cdot 6 + 7 \cdot 4 \), we should follow the order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
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First, calculate the multiplication parts:
- \( 2 \cdot 6 = 12 \)
- \( 7 \cdot 4 = 28 \)
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Now, substitute these values back into the expression: \[ 36 - 12 + 28 \]
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Next, perform the subtraction and addition from left to right:
- \( 36 - 12 = 24 \)
- \( 24 + 28 = 52 \)
Thus, the simplified result is: \[ \boxed{52} \]