Panel 3: Balancing by inspection

Unbalanced equation:

NH3 + O2 NO + H2O
Ammonia and oxygen yield nitric oxide and water.

Step 1: balance nitrogen atoms

After noting that nitrogen appears in only one reactant molecule, NH3, and one product molecule, NO, balance the nitrogen atoms.
1 NH3 + O2 1 NO + H2O

Step 2: balance hydrogen atoms

Since 3 hydrogen atoms appear in the reactants, there must be three hydrogens in the products. If the coefficient of ammonia reactant is 1, the coefficient of water product must be 3/2.
1 NH3 + O2 1 NO + 3/2 H2O

Step 3: balance oxygen atoms

There are 1+3/2=5/2 moles of oxygen atoms in the products. Making the coefficient of O2 equal to 5/4 will produce the same number of moles of oxygen in the reactants.
1 NH3 + 5/4 O2 1 NO + 3/2 H2O

Step 4: Obtain lowest whole number coefficients

Multiply all coefficients in the result of the previous step by 4.
4 NH3 + 5 O2 4 NO + 6 H2O