To solve the expression \( 36 \div 6 \cdot 2 + 1 \), we apply the order of operations (also known as PEMDAS/BODMAS):
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Division and Multiplication from left to right:
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First, calculate \( 36 \div 6 \): \[ 36 \div 6 = 6 \]
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Next, multiply the result by \( 2 \): \[ 6 \cdot 2 = 12 \]
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Now add \( 1 \): \[ 12 + 1 = 13 \]
Therefore, the expression \( 36 \div 6 \cdot 2 + 1 \) is equal to \( \boxed{13} \).