The radii of two planets A and B are R and 4R and their densities...

Acceleration due to gravity is written as $g = \dfrac{GM}{{r}^{2}} = \dfrac{G \times \dfrac{4}{3} \times \pi \times {r}^{3} \times ρ}{{r}^{2}} = \left(\dfrac{4\piG}{3}\right)ρr$

Given:

${r}_{A} = R{r}_{B} = 4R{ρ}_{A} = ρ{ρ}_{B} = \dfrac{ρ}{3}$

Hence, the ratio is

$\dfrac{{g}_{A}}{{g}_{B}} = \dfrac{R \times ρ}{4R \times \dfrac{ρ}{3}} = \dfrac{3}{4}$.