Step 1 (Oxidative Fusion):
$$2\text{MnO}_2 + 4\text{KOH} + \text{O}_2 \longrightarrow 2\text{K}_2\text{MnO}_4 + 2\text{H}_2\text{O} \quad (\text{Green Manganate Product})$$
Step 2 (Disproportionation):
$$3(\text{MnO}_4)^{2-} + 4\text{H}^+ \longrightarrow 2\text{MnO}_4^- + \text{MnO}_2 + 2\text{H}_2\text{O} \quad (\text{Purple Permanganate Product})$$
Oxidizing Actions Matrix:
$$\begin{aligned} \text{Acidic Medium:} &\quad \text{MnO}_4^- + 8\text{H}^+ + 5e^- \longrightarrow \text{Mn}^{2+} + 4\text{H}_2\text{O} \quad (\text{n-factor} = 5) \\ \text{Strongly Alkaline:} &\quad \text{MnO}_4^- + e^- \longrightarrow (\text{MnO}_4)^{2-} \quad (\text{n-factor} = 1) \\ \text{Faintly Alkaline / Neutral:} &\quad \text{MnO}_4^- + 2\text{H}_2\text{O} + 3e^- \longrightarrow \text{MnO}_2 + 4\text{OH}^- \quad (\text{n-factor} = 3) \end{aligned}$$