To solve the equation \(-5 (2x - 3) + 4x = -3x + 6\), we will first distribute the \(-5\) on the left side.
Starting with the left side:
\[ -5 (2x - 3) = -5 \cdot 2x + (-5) \cdot (-3) = -10x + 15 \]
Now, we can rewrite the equation:
\[ -10x + 15 + 4x = -3x + 6 \]
Next, we combine like terms on the left side:
\[ (-10x + 4x) + 15 = -3x + 6 \]
This simplifies to:
\[ -6x + 15 = -3x + 6 \]
Now, we isolate the \(x\) terms by adding \(6x\) to both sides of the equation:
\[ 15 = 3x + 6 \]
Next, we isolate the constant term by subtracting \(6\) from both sides:
\[ 15 - 6 = 3x \]
This simplifies to:
\[ 9 = 3x \]
Now, divide both sides by \(3\):
\[ x = 3 \]
Thus, the value of \(x\) that makes the equation true is:
\[ \boxed{3} \]