The equivalent weight of ${\mathrm{S}}_8\to {\mathrm{SO}}_4^{-2}$ (hypothetical) is written as $\frac{\mathrm{M}}{\mathrm{x}}$. What is the value of x.

The equivalent weight of ${\mathrm{S}}_8\to {\mathrm{SO}}_4^{-2}$ (hypothetical)

$\mathrm{Eq}. \mathrm{wt}. = \frac{\mathrm{molecular} \mathrm{mass}}{\mathrm{n}-\mathrm{factor}}$

n-factor of ${\mathrm{S}}_8\to {\mathrm{SO}}_4^{-2}$ is 48 because 

S was in 0 OS which goes to +6 OS hence or every S atom 6 electron transfer takes place so for 8 there will be 48 electron transfer takes place .

$\mathrm{Eq}. \mathrm{wt}. = \frac{\mathrm{M}}{48}$

hence option (c) that is x=48 is correct.