Be careful to capitalise your formulas correctly. MnO
2 is manganese dioxide, KMNO2 is nonsense. KMNO3 is also nonsense, and KMnO
3 does not exist (do you mean KMnO
4?).
The reactivity of MnO
2 in organic synthesis is covered in any textbook, and even in the
wikipedia article - it chomoselectively oxidises allylic alcohols.
The easiest way to start this problem is to identify which of those starting alcohols are optically active.