Test questions usually require regurgitating something already taught (whether that teaching is absolutely correct or not is not really an issue).
However, while it may be accurate, as the OP stated, that hydrogen peroxide always oxidizes ferrous ion to ferric, it is not incorrect to state that hydrogen peroxide also reduces ferric ion to ferrous.
How does this occur? Consider a beaker of ferric chloride to which is added some hydrogen peroxide:
Fe$^{3+}$ + H2O2 --> Fe$^{2+}$ + $^.$OOH + H$^+$
Fe$^{3+}$ + $^.$OOH --> Fe$^{2+}$ + H$^+$ + O2
These equations are the second and third from the question asked over a year ago (Ref 1). They amount to a hydrogen peroxide molecule going to O2, and 2 protons and two electrons reducing two ferric ions to ferrous. In the Fenton scheme, as the H2O2 runs out, the hydroperoxyl moiety will be the last oxidant in solution, since it is not as active as the hydroxyl radical, which will have been consumed too. So any ferric ions will be reduced to ferrous, but there will be no H2O2 to reoxidize the ferrous to ferric.
So H2O2 can reduce ferric ion to ferrous. Ferrous ions can be reoxidized to ferric only as long as some H2O2 is present:
Fe$^{2+}$ + H2O2 --> Fe$^{3+}$ + $^.$OH + OH$^-$
(the first equation in the question of Ref 1).
While the question may be questionable, with the above analysis, answers A and B could be correct. The pH is an important factor because at low pH, complexation of Fe$^{2+}$ occurs, limiting its ability to react with H2O2 (Ref 2).
Ref 1. Is the effect of hydroperoxyl radicals significant in the oxidation of organic compounds in the Fenton reaction? Why or why not?
Ref 2. https://en.wikipedia.org/wiki/Fenton%27s_reagent