To solve the equation \( -3(2x - 6) = -5 - (x - 8) \), we will first simplify both sides.
Step 1: Distribute on the left side
\[ -3(2x - 6) = -3 \cdot 2x + -3 \cdot -6 = -6x + 18 \]
So, the left side becomes:
\[ -6x + 18 \]
Step 2: Simplify the right side
The right side is:
\[ -5 - (x - 8) = -5 - x + 8 = 3 - x \]
So now the equation is:
\[ -6x + 18 = 3 - x \]
Step 3: Arrange the equation
To get all \(x\) terms on one side and the constants on the other side, add \(x\) to both sides:
\[ -6x + x + 18 = 3 \]
This simplifies to:
\[ -5x + 18 = 3 \]
Step 4: Isolate the \(x\) term
Now, subtract 18 from both sides:
\[ -5x = 3 - 18 \] \[ -5x = -15 \]
Step 5: Solve for \(x\)
Now, divide both sides by -5:
\[ x = \frac{-15}{-5} = 3 \]
So, the solution is:
\[ \boxed{3} \]