Redoing the problem
I did it again by starting with an actual balanced equation
Ok, starting with the original equation (now balanced):
MnO_4^-+8S^{2-}\xrightarrow{}MnO_2+S_8
I then separate into two "half-reactions":
MnO_4^-\xrightarrow{}MnO_2
8S^{2-}\xrightarrow{}S_8
Figureing the oxidation charge for the left side of the first "half-reaction":
X-8+1=0\xrightarrow{}X=7
Therefore, the oxidation number of Mn on the left side is 7, right?
Then I do the right side of the first "half-reaction":
X-4=0\xrightarrow{}X=4
This means that the oxidation number of Mn on the right side is 4. Meaning that I have to add 3 electrons to the left side of the first "half-reaction" equation, right?:
MnO_4^-+3e^-\xrightarrow{}MnO_2
Now, I added H+ ions to the left side to bring it's overall charge down to zero, because the right side has an overall charge of zero:
MnO_4^-+3e^-+4H^+\xrightarrow{}MnO_2
Finally, I add H2O to even out the oxygens in the first "half-reaction" equation:
MnO_4^-+3e^-+4H^+\xrightarrow{}MnO_2+2H_2O
Going on to the second of the two "half-reaction" equations:
8S^{2-}\xrightarrow{}S_8
The oxidation number for the left hand side of the second "half-reaction" equation is -2 and for the right side it is 0, right? So then I added 2 electrons to the right side of the second "half-reaction" equation:
8S^{2-}\xrightarrow{}S_8+2e^-
I then multiply the two results from the "half-reaction" equations in order to eliminate the electrons:
(MnO_4^-+3e^-+4H^+\xrightarrow{}MnO_2+2H_2O)*2=2MnO_4^-+6e^-+8H^+\xrightarrow{}2MnO_2+4H_2O
(8S^{2-}\xrightarrow{}S_8+16e^-)*3=24S^{2-}\xrightarrow{}3S_8+48e^-
Adding them together, I get:
2MnO_4^-+24S^{2-}+8H^+\xrightarrow{}2MnO_2+3S_8+4H_2O
Finally, I add OH- to balance and eliminate the H2O's on the right side:
2MnO_4^-+24S^{2-}+8H^++8OH^-\xrightarrow{}2MnO_2+3S_8+4H_2O+8OH^-
2MnO_4^-+24S^{2-}+8H_2O\xrightarrow{}2MnO_2+3S_8+4H_2O+8OH^-
2MnO_4^-+24S^{2-}+4H_2O^+\xrightarrow{}2MnO_2+3S_8+8OH^-
Does this seem reasonable?