To evaluate the expression \( 17 - 2 \times 6 + 2^2 \), we will follow the order of operations (often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
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Calculate the exponent: \[ 2^2 = 4 \]
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Then perform the multiplication: \[ 2 \times 6 = 12 \]
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Now substitute these values back into the expression: \[ 17 - 12 + 4 \]
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Next, perform the subtraction and addition from left to right: \[ 17 - 12 = 5 \] \[ 5 + 4 = 9 \]
The final result is: \[ \boxed{9} \]