The mass of the crucible is given as 18.2 g. The mass of the crucible + mass of the silicon is 18.48 g.
This gives the mass of the silicon alone as 18.48 - 18.20 = 0.28 g.
The mass of the crucible and the silicon oxide is 18.80 g
This gives the mass of the silicon oxide as 18.8 - 18.2 = 0.6 g
So we have 0.28 g of silicon reacting with 0.6 - 0.28 = 0.32 g of oxygen to give the silicon oxide.
The ratio of the molar mass of oxygen to the molar mass of silicon is 16 : 28. From what we have found above, that 0.32 g of oxygen reacts with .28 g of silicon, we can say that the molecular formula of the silicon oxide is SiO2.
The required empirical formula of the silicon oxide is SiO2.