If in doubt you may try to balance knowing that in general oxidizers like MnO4- or CrO4-2 (Cr2O7-2) are effecitve in low pH, Cl2, ClO- - in basic. But then MnO4- works in basic (it gets reduced to MnO4-2), in neutral (MnO2) and acidic (Mn2+), so this approach can require additional information.
Permanganate you already know, chromate or dichromate goes to Cr+3, chlorine (bromine, iodine) to Cl-. These are most common, others require more experience - and the only more or less sure method of finding out products is to check redox potentials in tables. But even that can be misleading.