Let x be the oxidation number of Br.
Oxygen has an oxidation number of -2. There are two oxygen atoms in BrO-2, so the total contribution from oxygen is 2 × (-2) = -4.
To balance the overall charge of the ion, which is -2, the oxidation number of Br must be:
x + (-4) = -2
x = -2 + 4
x = +2
Therefore, the oxidation number of Br in BrO-2 is +2.