Statement 1=> 8k is divisible by 16.
$$\frac{8k}{16}=\frac{k}{2}$$
Hence, k is a multiple of 2
If k=6, then k is not divisible by 4
If k=8, then k is divisible by 4
The information provided is not enough to arrive at a definite answer, hence statement 1 is NOT SUFFICIENT.

Statement 2=>
9k is divisible by 12
$$\frac{9k}{12}=\frac{3k}{4}\ =\ \frac{3}{1}\cdot\frac{k}{4}$$
Hence, k is a multiple of 4.
If k=8, then k is divisible by 4
If k=12, then k is divisible by 4
Hence, statement 2 is SUFFICIENT.

Since statement 2 alone is SUFFICIENT, the answer is, therefore, option B.