Balancing Chemical Equations

Chemical equations are very important for written Chemistry, for example, if we take Methane + Oxygen -> Carbon Dioxide + Water, the underlined words are products, while the non-underlined are not.

Now to write this as chemical symbols you would write it as:
c
the Ch4 is because there is 1 carbon and 4 hydrogen. For the O2 it is because O2 is 2 oxygens.
While the products CO2 + H2O, has the CO2 has 1 carbon and 2 oxygen, while H2O has 2 hydrogen and 1 oxygen. 

Now if you want to "balance" these equations, it is mainly done by trial and error, it is because you can't change the subscripts because it changes the whole element to a completely different one.
But we can change how many of the elements there can be, to balance the
Ch4 + O2  -> CO2 + H2O.
In order to make the equation "balanced" we must match the number of oxygen atoms at both sides.
So if we look at the reactants we might notice