9 : 8 :: 16 : ?

The answer is $\boxed{27}$.

In the proportion $9:8::16:x$, the first and third terms are in the ratio $9:16$, and the second and fourth terms are in the ratio $8:x$. Therefore, $x$ must be the number that, when divided by $8$, gives $9$, and when divided by $16$, gives $8$. This number is $27$.

Here is a more detailed explanation of each option:

• Option A: $27$. This is the correct answer.
• Option B: $17$. This is not the correct answer because $17$ is not in the ratio $9:16$.
• Option C: $16$. This is not the correct answer because $16$ is not in the ratio $8:x$.
• Option D: $18$. This is not the correct answer because $18$ is not in the ratio $9:16$ or $8:x$.