Potassium oxide is an ionic compound. The potassium has a charge of K+ and oxygen has a charge of O2−. We need 2 potassium ions to balance one oxide ion making the formula K2O.
Potassium hydroxide is an ionic compound. The potassium has a charge of K+ and hydroxide has a charge of OH−. We need 1 potassium ion to balance one hydroxide ion making the formula KOH.
K2O+ H2O→KOH
To balance the equation we place a coefficient of 2 in front of the potassium hydroxide.
K2O+H2O→2KOH
I hope this was helpful.