Okay, let's look at the oxidation number of each substance.
-Br2 has an oxidation number of 0 because it is in a stable form.
- I- has a -1 charge and thus has an oxidation number of -1.
- 2Br- has a -1 charge also
- I2 has an oxidation number of 0 as well.
Bromine goes from 0 to -1 and Iodine goes from -1 to 0.
Therefore, Bromine is having an electron added whilst Iodine is having an electron removed.
Oxidation is Loss of electrons so Iodine is being oxidised, Reduction is Gain of electrons so Bromine is being reduced.
