To solve the equation \(-4k + 2(5k - 6) = -3k - 39\), let's first distribute the \(2\) on the left side:
\[ -4k + 2(5k) - 2(6) = -3k - 39 \]
This simplifies to:
\[ -4k + 10k - 12 = -3k - 39 \]
Now, combine like terms on the left side:
\[ (10k - 4k) - 12 = -3k - 39 \]
Which gives us:
\[ 6k - 12 = -3k - 39 \]
Next, we can add \(3k\) to both sides to get all \(k\) terms on one side:
\[ 6k + 3k - 12 = -39 \]
This results in:
\[ 9k - 12 = -39 \]
Now, add \(12\) to both sides:
\[ 9k = -39 + 12 \]
Which simplifies to:
\[ 9k = -27 \]
Now, divide both sides by \(9\):
\[ k = \frac{-27}{9} = -3 \]
Thus, the solution is:
\[ \boxed{-3} \]