KMnO₄ has an overall neutral charge, so that means that the total oxidation numbers should sum up to 0.
Oxygen will almost always have an oxidation number of -2, and K, because it is a group 1A metal, has an oxidation number of +1
There are 4 oxygens so the total oxidation number is 4*-2 = -8 And K has an oxidation number of +1
We are trying to find out the oxidation number of Mn. Remember since our compound is neutral, the sum of the oxidation numbers should be 0. So if we call the oxidation number of Mn as X, we then know that