The chemical equation for the reaction of magnesium chloride and potassium hydroxide is:

$$MgCl_2 + 2KOH → Mg(OH)_2 + 2KCl$$

In this reaction, magnesium chloride reacts with potassium hydroxide to form magnesium hydroxide and potassium chloride. Magnesium hydroxide is a white precipitate, while potassium chloride is a soluble salt.