The oxidation number of  in ${\mathrm{S}}_2{\mathrm{O}}_8^{2-}$ is:

If O.N. of S in ${\mathrm{S}}_2{\mathrm{O}}_8^{2-}$ is x then:

$2\left(\mathrm{x}\right)+8(-2)=-2$ $\mathrm{x}=+7$ but O. N. of S can not exceed +6.

This means that there is peroxide linkage in the ${\mathrm{S}}_2{\mathrm{O}}_8^{2-}$, its structure is:

Oxidation state of S in ${\mathrm{S}}_2{\mathrm{O}}_8^{2-}$

$$\begin{gathered} 2\left(\mathrm{x}\right)+6\left(-2\right)+2\left(-1\right)=-2 \\ 2\mathrm{x}-12-2=-2 \\ \mathrm{x}=+6 \end{gathered}$$