How would you balance the equation KOH + Ca(OH)2 ?

No reaction will take place when potassium hydroxide is mixed with calcium hydroxide.

Thus, KOH + Ca(OH)2 ---> no reaction

This is because both potassium and calcium are metals and will dissociate to form cations. The only anions are hydroxide ions, however. Hence, the possible new compounds are also the hydroxides of potassium and calcium. Thus, no reaction will take place and we don't have an equation to balance. 

If we mix potassium hydroxide and calcium chloride, we will have a reaction, which can be written as

KOH + CaCl2 -> KCl + Ca(OH)2

This equation is not balanced, since the number of atoms of each species should be the same on both sides of the equation. Here, chlorine (Cl), hydrogen (H) and oxygen (O) are not balanced.

The well balanced equation for this reaction is:

`2KOH + CaCl2 -> 2KCl + Ca(OH)2`

We can check that all the species have the same number of atoms on the reactant and product side and hence the equation is balanced.

Hope this helps.