12, 18 and $x$ are in continued proportion. The value of $x$ is :

Given,

12, 18 and $x$ are in continued proportion.

We know that,

If $a, b$ and $c$ are in continued proportion, then $b^2 = ac$.

$$\begin{aligned}\Rightarrow 18^2 = 12 \times x \\[1em] \Rightarrow 324 = 12x \\[1em] \Rightarrow x = \frac{324}{12} \\[1em] \Rightarrow x = 27.\end{aligned}$$

Hence, option 2 is the correct option.