Let Sulphur be
x
. Oxygen has a -2 oxidation state, therefore:
4
⋅
x
+
6
⋅
(
−
2
)
=
−
2
→
because the net charge of the ion is -2)
Solving for
x
will give you
x
=
2.5
→
that Is the formal charge on each S atom.
Now, In
S
2
O
2
−
3
, you have
2
x
−
6
=
−
2
x
=
2
Therefore change In oxidation state Is
2.5
−
2
=
0.5
Hence the net change due to 4 atoms is
4
⋅
0.5
=
2