The order of size is:

As we go from left to right in a periodic table, the atomic radius of an atom decreases due to addition of an extra proton which leads to stronger pull of electrons while extra electron goes to the same principal energy level.

While going down in a group, an extra energy level adds to the structure which leads to increase in atomic radius. Thus, on moving down the group, atomic radius increases.

Now, out of the given ions, S^2- and O^2- belongs to group 16 and Cl^- and F^- belongs to group 17.

Thus, the size of group 17 ions would be smaller than group 16 ions.

Next, on moving down the group, size increases, thus S^2-> O^2- and Cl^-> F^-.

But period 1 (O^2-, F^-)atoms are smaller than period 2 (S^2-,Cl^-)atoms

Therefore, considering all the factors, the correct order of size is:

${\mathrm{S}}^{2-} >{\mathrm{Cl}}^{-} >{\mathrm{O}}^{2-} >{\mathrm{F}}^{-}$