$Y=\frac{\frac{F}{A}}{\frac{l}{L}}=\frac{F\times L}{A\times l}$   [$l$ = Change in length, $L$ = Original length] (where $Y$ is Young's modulus of elasticity)

Since $Y$, $L$ and $A$ remain same.
$\Rightarrow F\propto l$
$\Rightarrow \frac{F_1}{F_2}=\frac{l_1}{l_2}$
$\Rightarrow \frac{F}{F_2}=\frac{2\times {10}^{-3}}{4\times {10}^{-3}}$

$$\begin{gathered} \Rightarrow F_2=2F \\ \Rightarrow F_2=nF \\ \Rightarrow n=2 \end{gathered}$$