How do you balance #HCl + Ca(OH)_2 -> H_2O + CaCl_2#?
You balance it stoichiometrically, and in fact you have almost done it.
"Stoichiometric" is a word that simply means "in the right measure". You practise stoichiometry every time you make a cash or an electronic transaction. The money that you extract from a cash machine (the credit item), must match the debit amount that is made to your personal account.
How does this apply to your question? Well, simply because since mass is conserved in every chemical reaction, and atoms and molecules have definite masses, (i) the mass of reactants MUST equal the mass of products, and thus (ii) for every atom on the reactant side, there MUST be a corresponding atom on the product side.
So you have hydrochloric acid, and calcium hydroxide, a common base that requires 2 equivalents of acid for stoichiometric reaction:
Does this reaction demonstrate stoichiometry? Please do not trust my arithmetic.
In fact, we can even be more concise than this because the calcium salts are present in solution as
Accordingly, we could write the net ionic equation as,
We must still observe stoichiometry, and remember that the molar quantity of calcium hydroxide is HALF the molar quantity of hydroxide ion. In addition, not only is mass conserved, but charge is conserved. Capisce?