According to the conversation of mass, mass cannot be created or destroyed. This means whatever is done to one side, must be done to the other.
There are 4 Phosphorus atoms on the left, there must be 4 on the right. To do this, you must multiply the P2O3 by 2 to get 4 Phosphorus atoms and 6 Oxygen atoms. Now to balance the Oxygen atoms, you must multiply the oxygen atoms on the left by 3.
1 P4 + 3 O2 —-> 2 P2O3
Lastly, this equation type is synthesis (combination) because two reactants are becoming a single product.
