To simplify the expression \( 2(k - 4) - 3(2k - 1) \), we can follow these steps:
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Distribute the \( 2 \) in the first term: \[ 2(k - 4) = 2k - 8 \]
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Distribute the \( -3 \) in the second term: \[ -3(2k - 1) = -6k + 3 \]
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Now, substitute these back into the expression: \[ 2(k - 4) - 3(2k - 1) = (2k - 8) + (-6k + 3) \]
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Combine like terms: \[ 2k - 6k - 8 + 3 = -4k - 5 \]
Thus, the simplified result is: \[ \boxed{-4k - 5} \]