Let's balance the reaction step by step:
- First, balance the sulfur atoms:
On the left side, there are 8 sulfur atoms in \( S_8 \), and on the right side, we have 1 sulfur atom in \( S^{2-} \) and 2 in \( S_2O_3^{2-} \). Thus, the number of sulfur atoms on the right is 4 from \( S_2O_3^{2-} \) and 4 from \( S^{2-} \). So, we will have \( x = 1 \) and \( z = 4 \).
- Next, balance the oxygen atoms:
On the right, there are 6 oxygen atoms from the \( 6H_2O \) molecules and 6 from the \( 2S_2O_3^{2-} \) ions. The total number of oxygen atoms on the left will match with \( y = 12 \).
Thus, the values are:
\[
x = 1, \, y = 12, \, z = 4
\]
So the correct answer is \( \boxed{1, 12, 4} \).