With molecular compounds, prefixes are used (mono, di, tri, etc).
Let's break this compound apart (not literally):
dinitrogentrioxide
We know nitrogen is represented as 'N'
We also know that oxygen is represented as 'O'
'Di' means 2, and 'tri' means 3
Let's put everything together now:
N2 (dinitrogen)
O3 (trioxide)
Final answer: N2O3