Balancing chemical equations by inspection

Consider the reaction of methane (CH4) with oxygen to give carbon dioxide and water.
Step 1:
The equation must use correct formulae and have the form reactants products.
 
CH4 + O2 CO2 + H2O
 
Step 2:
Count the numbers of each type of atom in reactants in products.
 
1 C 4 H and 2 O (reactants)  1 C 2 H 3 O (products)

Step 3: Balance the element that occurs in the fewest formulae by changing the coefficient in one or more of these. 
If there is more than one element in this category, choose an element other than oxygen or hydrogen. 

No change required above. C is balanced

Step 3: Then balance the one of the remaining atoms that occurs least often.
 
H is chosen because it is in one reactant and one product.

CH4 + O2 CO2 + 2H2O
1 C and 4 H and 2 O  1 C and 4 H and 4 O

Step 3: Continue by balancing any remaining atoms.
 
CH4 + 2O2 CO2 + 2H2O
1 C and 4 H and 4 O   1 C and 4 H and 4 O