Why is it important to learn how to balance a chemical equation?
Why? Because mass is conserved in every chemical reaction.
Before ideas of atoms and molecules were developed, chemists and apothecaries were well aware that chemical reactions conserved mass. A chemist started with 10 g of reactant; the chemist would inevitably finish with close enough to 10 g of product. Apparent contradictions of the law of conservation of mass, for instance that we get more mass after a combustion reaction, were resolved by the realization that gases, in particular oxygen, were massive particles, and these masses contributed to, and should be included in the reaction. And of course, the recognition that masses were conserved influenced early and later atomic theories.
See this old answer.
So how do you balance chemical reactions? The simple answer is with difficulty. Nevertheless, you have already have practice with stoichiometry. When you go to a shop and buy something, and you hand over a note, the value of the note MUST equal the value of the item + the value of your change. When you buy something electronically, the credit placed on the vendor's account MUST equal the debit made to your account. Of course sometimes they don't add up; that's when you end up in call queue to complain about the $99-00 debit made to your account for your $9-99 purchase; this is a simple and common accounting error so I am told.
And thus when you are given an equation, you are generally told or have an idea of what the produts are. Hydrocarbon combustion is a good example. Hydrocarbons combust with oxygen to give stoichiometric carbon dioxide and water.
Combustion of hexanes:
Now clearly this is unbalanced. To make it stoichiometric, we (i) balance the carbons,
And then the hydrogens:
And then the oxygens: