What is the oxidation state of S in ##S_2O_3^-2##?

2+

You should make sure to get this down solid, its important. Oxygen is always 2-, and hydrogen is mostly 1- (there are some cases like water where it is 1+).

You add all the charges of the atoms to get the overall charge of the molecule.

So, ##S_2O_3^(-2) = 2S*(charg e) + 3O*(2-) = -2## ##2(charg e) + -6 = -2## ##(charg e) = -4/2 = -2##