Let $\(n=3 k\)$ for some integer $k$.
Test each expression
- (A) $\(3 n=9 k\)$.
$\(9 k\)$ is not always a multiple of 12 (e.g., \($k=1 \Rightarrow 9\)$ ), so not required.
- (B) $\(4 n=12 k\)$.
$\(12 k\)$ is always a multiple of 12 , so this must be a multiple of 12 .
- (C) $\(n^2+12=9 k^2+12\)$.

For $\(k=1\)$, this is $\(9+12=21\)$, not a multiple of 12 , so not required.
- (D) $12 n=36 k$.
$\(36 k\)$ is always a multiple of 12 , so this must be a multiple of 12 .
Correct choices: (B) and (D).