According to the question,

3 men can do a piece of work in 18 days. 6 children can also do that work in 18 days.

 So, 3 men =6 children

⇒ 1 man = 2 children

∴ 4 men + 4 children (2 men)

⇒ 4 men + 2 men = 6 men

Here,

M₁ = 3, D₁ =18, W₂ =1

M₂ = 6, D₂ = ?, W₁ = 1

So according to the formula,

     M₁ D₁ W₂ = M₂ D₂ W₁

$$\begin{gathered} \Rightarrow 3\times 18\times 1=6\times D_2\times 1 \\ \therefore D_2=\frac{3\times 18}{6}=9 days \end{gathered}$$

 Hence option D is correct.