The point $(a, b)$ lies on the line with the equation $3x + 2y = 12.$ When $a = 4$, what is the value of $b$?
We plug in $x = 4$: \begin{align*}
3(4) + 2y &= 12\\
12 + 2y &= 12\\
y &= 0.
\end{align*}

Therefore, $b = \boxed{0}$.