Step 1: Write the structure of tetrathionate ion.
The ion
\[
S_4O_6^{2-}
\]
contains a chain of four sulphur atoms.
Its structure can be represented as
\[
O_3S-S-S-SO_3^{2-}
\]
The two terminal sulphur atoms are bonded to oxygen atoms, while the two middle sulphur atoms are connected only with sulphur atoms.
Step 2: Find oxidation state of terminal sulphur atoms.
Each terminal sulphur atom is attached to three oxygen atoms.
Since oxygen has oxidation number
\[
-2
\]
the total contribution from oxygen atoms attached to one terminal sulphur is
\[
3\times (-2)=-6
\]
The sulphur atom balances this and effectively has oxidation state
\[
+5
\]
Thus, the two terminal sulphur atoms have oxidation number
\[
+5
\]
Step 3: Find oxidation state of middle sulphur atoms.
The two middle sulphur atoms are connected only through
\[
S-S
\]
bonds.
Since bonds between identical atoms contribute zero to oxidation number, each middle sulphur atom has oxidation number
\[
0
\]
Step 4: Verify the total charge.
Adding all oxidation numbers:
\[
(+5)+0+0+(+5)=+10
\]
For six oxygen atoms:
\[
6\times (-2)=-12
\]
Total charge:
\[
+10-12=-2
\]
which matches the charge on the ion.
Step 5: Final conclusion.
Therefore, the oxidation numbers on the sulphur atoms are
\[
\boxed{5,\,0,\,0,\,5}
\]