Write the balanced equation for each step in the mechanism:
NO(g) + Br₂(g) --> NOBr₂(g)
NOBr₂(g) + NO(g) --> 2 NOBr(g)
Write all reactants in all steps on the left of a reaction arrow. Write all products on the right.
NO(g) + Br₂(g) + NOBr₂(g) + NO(g) --> NOBr₂(g) + 2 NOBr(g)
Cancel any formulas that appear on both sides of the arrow and, if a formula appears more than once, use a coefficient.
NO(g) + Br₂(g) + NOBr₂(g) + NO(g) --> NOBr₂(g) + 2 NOBr(g)
(A reaction intermediate is formed in an earlier step and reacted away in a later step, so the cancelled formulas in this case are the intermediate, NOBr₂(g), which was formed in step one and reacted in step 2.)
The overall equation is
2 NO(g) + Br₂(g) --> 2 NOBr(g)