To simplify the expression \( 4 - 16 + 2 \), we follow the order of operations, which involves performing addition and subtraction from left to right.
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Start with the first two terms: \[ 4 - 16 = -12 \]
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Now add the next term: \[ -12 + 2 = -10 \]
Thus, the fully simplified expression is: \[ \boxed{-10} \]