3 C-IIH3C-IIH2OH + 2 KMnVIIO4 3 C-IIIH3CIHO + 2 MnIVO2 + 2 KOH + 2 H2O

This is an oxidation-reduction (redox) reaction:

2 MnVII + 6 e- 2 MnIV (reduction)

3 C-II - 9 e- 3 CI (oxidation)

3 C-II + 3 e- 3 C-III (reduction)

Change the oxidation states