Let's solve the equation step by step:
Given: \[ -3(-2x - 3) - 3x + 4 = -2 \]
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Distribute \(-3\) on the left side: \[ -3 \cdot -2x + -3 \cdot -3 - 3x + 4 = -2 \] This simplifies to: \[ 6x + 9 - 3x + 4 = -2 \]
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Combine like terms on the left side: \[ (6x - 3x) + (9 + 4) = -2 \] This simplifies to: \[ 3x + 13 = -2 \]
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Now, isolate \(3x\) by subtracting 13 from both sides: \[ 3x = -2 - 13 \] This simplifies to: \[ 3x = -15 \]
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Divide both sides by 3 to solve for \(x\): \[ x = -5 \]
Thus, the solution to the equation is: \[ \boxed{-5} \]