Answer
The second satellite takes 128 hours to orbit Jupiter.
Work Step by Step
When a satellite orbits a planet, the gravitational force provides the centripetal force to keep the satellite moving in a circle. Let $M_p$ be the mass of the planet and let $M_s$ be the mass of the satellite. We can find an expression for the angular speed of a satellite:
$\frac{G~M_p~M_s}{R^2} = M_s~\omega^2~R$
$\omega = \sqrt{\frac{G~M_p}{R^3}}$
We can find an expression for a satellite's orbital period $P$:
$P = \frac{2\pi}{\omega} = 2\pi~\sqrt{\frac{R^3}{G~M_p}}$
We can find an expression for the period $P_1$ of the first satellite:
$P_1 = 2\pi~\sqrt{\frac{r^3}{G~M_p}} = 16~h$
We can find the period $P_2$ of the other satellite:
$P_2 = 2\pi~\sqrt{\frac{(4.0~r)^3}{G~M_p}}$
$P_2 = 8\times 2\pi~\sqrt{\frac{r^3}{G~M_p}}$
$P_2 = 8\times P_1$
$P_2 = (8)(16~h)$
$P_2 = 128~h$
The second satellite takes 128 hours to orbit Jupiter.
