The mean proportional between 4 and 9 is :

Let x be the mean proportional between 4 and 9 then,

$$\begin{aligned}\Rightarrow \frac{4}{x} = \frac{x}{9} \\[1em] \Rightarrow x^2 = 4 \times 9 \\[1em] \Rightarrow x^2 = 36 \\[1em] \Rightarrow x = \sqrt{36} = 6.\end{aligned}$$

Hence, Option 2 is the correct option.