You could assume that but it doesn't fit with the information given. Metals are the easiest to start with, in this case Mn(4+)---->Mn(2+) Gains Electrons Reduced = Oxidant. HCl is easy to eliminate since Cl is minus one on both sides and H is (1+) on both sides, POE gives you D.
To answer your question, H2O, OH-, & H+ are (95% of the time) used for balancing the half reactions. In this case:
Recduction Half Reaction: MnO2 + 2e- + 2HCl ---> MnCl2 + 2OH-
Oxidation Half Reaction: ..H2O2 + 2OH- ---> O2 + 2e- + 2H2O
Which Gives: HCL + H2O2 + MnO2 -> MnCL2 + O2 + 2-H2O (the OH-'s cancel and the e-'s cancel when you add the two half reactions)
You'll have to look in your Gen Chem text since, from what i've seen, EK and TPR don't address balancing Redox RXN's. Hope that helps.