use the O.N method: http://www.chemicalforums.com/index.php?board=2;action=display;threadid=4204

as an alternative u could try balancing the elements instead (thats what i do all the time to balance equations)

So try this one:

KMnO₄ + H₂O₂ + H₂SO₄ -> O₂ + MnSO₄ + H₂O + K₂SO₄

or much simplified form, with all spectators removed, so you may concentrate on the real problem:

MnO₄^- + H₂O₂ + H⁺ -> O₂ + Mn²⁺ + H₂O

first balance H and then O' you'll come to:

MnO4(-) + H2O2 + H(+) --> 2,25 O2 + Mn(2+) + 1,5 H2O

then multiply with 4

Which gives

4MnO₄^- + 4H₂O₂ + 4H⁺ --> 9O₂ + 4Mn²⁺ + 6H₂O

why not

4MnO₄^- + 2H₂O₂ + 4H⁺ --> 8O₂ + 4Mn²⁺ + 4H₂O

or

4MnO₄^- + 6H₂O₂ + 4H⁺ --> 10O₂ + 4Mn²⁺ + 8H₂O?

Also note that charge is not balanced.

second and third are incorrect because the coefficients are not the lowest possible --> divide by 2.

OK. Dividing by two gives:

2MnO₄^- + H₂O₂ + 2H⁺ --> 4O₂ + 2Mn²⁺ + 2H₂O

or

2MnO₄^- + 3H₂O₂ + 2H⁺ --> 5O₂ + 2Mn²⁺ + 4H₂O

plus your original:

4MnO₄^- + 4H₂O₂ + 4H⁺ --> 9O₂ + 4Mn²⁺ + 6H₂O

Apart from the fact that they are all wrong due to ubalanced charge - they are balanced with respect to all elements, they are also "correct" as they are using lowest possible coeffcients.

Yet they can't be all correct - so perhaps the method is wrong?