Two point charges 8 \, μ C and -2 \, μ C are located at x = 2 cm...

According to Gauss's law, the electric flux through a closed surface is given by $\Phi = \dfrac{q_{\text{enclosed}}}{\varepsilon_0}$.

For the first sphere of radius $r_1 = 3$ cm centered at the origin, only the charge at $x = 2$ cm is enclosed.

$q_{\text{enclosed}, 1} = 8 \, \mu\text{C}$

$\Phi_1 = \dfrac{8 \, \mu\text{C}}{\varepsilon_0}$

For the second sphere of radius $r_2 = 5$ cm centered at the origin, both charges at $x = 2$ cm and $x = 4$ cm are enclosed.

$q_{\text{enclosed}, 2} = 8 \, \mu\text{C} - 2 \, \mu\text{C} = 6 \, \mu\text{C}$

$\Phi_2 = \dfrac{6 \, \mu\text{C}}{\varepsilon_0}$

The ratio of the electric flux is:

$\dfrac{\Phi_1}{\Phi_2} = \dfrac{8}{6} = \dfrac{4}{3}$

Answer: $4 : 3$