$\Delta x=\frac{F L}{A Y}$

For wire $A$

$\Delta L_A=\frac{F \cdot L_A}{\pi r_A^2 \cdot Y_A} \ldots (1)$

For wire $B$

$\Delta L_B=\frac{F \cdot L_B}{\pi r_B^2 \cdot Y_B} \ldots (2)$

Divide $(1)$ by $(2)$

$\frac{\Delta L_A}{\Delta L_B}=\frac{F \cdot L_A}{\pi r_A^2 \cdot Y_A} \times \frac{\pi r_B^2 \cdot Y_B}{F \times L_B}=\frac{L_A}{L_B} \times\left(\frac{r_B}{r_A}\right)^2 \times \frac{Y_B}{Y_A}$

Substituting the value of ratio's

$\frac{\Delta L_A}{\Delta L_B}=\frac{4}{1} \times\left(\frac{1}{3}\right)^2 \times \frac{2}{1}=\frac{8}{9}$