To solve the equation \( 3(3y - 12) = 0 \), we can start by dividing both sides by 3:
\[ 3y - 12 = 0 \]
Next, we add 12 to both sides:
\[ 3y = 12 \]
Now, we divide both sides by 3:
\[ y = 4 \]
Thus, the value of \( y \) is \( 4 \).
So, the correct choice is \( 4 \).