To solve the equation
\[ \frac{1}{2} (8x - 6) = x - 12, \]
first, remove the fraction by multiplying both sides of the equation by 2:
\[ 8x - 6 = 2(x - 12). \]
Next, distribute the 2 on the right side:
\[ 8x - 6 = 2x - 24. \]
Now, isolate the variable \(x\) by first moving all terms involving \(x\) to one side and constant terms to the other side. Subtract \(2x\) from both sides:
\[ 8x - 2x - 6 = -24. \]
This simplifies to:
\[ 6x - 6 = -24. \]
Next, add 6 to both sides to isolate the term with \(x\):
\[ 6x = -24 + 6, \]
which simplifies to:
\[ 6x = -18. \]
Finally, divide both sides by 6:
\[ x = -3. \]
Thus, the value of \(x\) is
\[ \boxed{-3}. \]