You may teach me about the preparation in chemistry like potassium manganese

Manganese dioxide is fused with potassium hydroxide ($\text{KOH}$) and an oxidizing agent like potassium chlorate ($\text{KClO}_3$) or air. This reaction produces green potassium manganate.

$$2\text{MnO}_2 + 4\text{KOH} + \text{O}_2 \xrightarrow{\text{Heat}} 2\text{K}_2\text{MnO}_4 + 2\text{H}_2\text{O}$$

Potassium manganate can be oxidized to potassium permanganate either chemically or electrolytically.

• Chemical Oxidation: The green potassium manganate solution is treated with a weak acid (like $\text{CO}_2$ or dilute $\text{H}_2\text{SO}_4$) or chlorine. This disproportionation reaction yields purple potassium permanganate and manganese dioxide. $$3\text{K}_2\text{MnO}_4 + 2\text{H}_2\text{O} + 4\text{CO}_2 \longrightarrow 2\text{KMnO}_4 + \text{MnO}_2 + 4\text{KHCO}_3$$
• Electrolytic Oxidation: This is the preferred industrial method. An alkaline solution of potassium manganate is electrolyzed. Manganate ions ($\text{MnO}_4^{2-}$) are oxidized to permanganate ions ($\text{MnO}_4^-$) at the anode. $$\text{MnO}_4^{2-} \longrightarrow \text{MnO}_4^- + \text{e}^-$$

The overall process yields $\text{potassium permanganate}$.