To solve the equation
\[ -3(-x - 2) + 3x + 4 = -44, \]
let's start by distributing the \(-3\) into the expression \(-x - 2\):
\[ -3(-x) - 3(-2) + 3x + 4 = -44. \]
This simplifies to:
\[ 3x + 6 + 3x + 4 = -44. \]
Now, combine like terms:
\[ 3x + 3x + 6 + 4 = -44, \] \[ 6x + 10 = -44. \]
Next, subtract \(10\) from both sides of the equation:
\[ 6x + 10 - 10 = -44 - 10, \] \[ 6x = -54. \]
Now, divide both sides by \(6\):
\[ x = \frac{-54}{6}, \] \[ x = -9. \]
Thus, the solution for \(x\) is
\[ \boxed{-9}. \]