A lot depends on the details, but this is basically a simple stoichiometry and some simple algebra, nothing more complicated than - say - calculating circle area from a given radius.

Ask for the concentrations of Mn^{2+} and Fe^{2+}, add them, multiply by 3.9 as suggested, you have your answer (volume per volume, you may need some additional concentration calculations, again nothing more complicated).

Trick is, 3.9 is probably more or less optimal for a given Mn/Fe ratio in the incoming water, sadly I don;t see this information in the paper. I just skimmed though.