What kind of reaction is 2H2O2 2H2O plus O2?

2H2O2 <-> H2O + O2

the oxidation number of each O in H2O2 is -1

the oxidation number in H2O is -2

the oxidation number in O2 is zero.

The average oxidation number of oxygen atoms on both sides of the equation. is the same. So overall the net change to oxygen is zero one is reduced two are oxidised.

Looked at from the viewpoint of the oxygen atoms in O2 they started off with oxidation number of -1 and have ended up with 0, so they have been oxidised. (oxidation is loss of electrons, and therefore an increase in oxidation number.)