To solve the equation \( 12(4x - 4) = x + 3 \), we start by distributing the 12 on the left side:
\[ 12 \cdot 4x - 12 \cdot 4 = x + 3 \] \[ 48x - 48 = x + 3 \]
Next, we'll isolate \( x \). Start by subtracting \( x \) from both sides:
\[ 48x - x - 48 = 3 \] \[ 47x - 48 = 3 \]
Now, add 48 to both sides:
\[ 47x = 3 + 48 \] \[ 47x = 51 \]
Finally, divide both sides by 47:
\[ x = \frac{51}{47} \]
Thus, the solution is:
\[ x = \frac{51}{47} \]