The quantities you have to know are the molar masses and the molecular stoichiometric ratios. The solution for this problem is as follows:
Mass Percent of Iodine = (Mass of Iodine/Mass of NaBr and KI)*100
Mass of NaBr = 1 mol NaBr * 102.89 g/mol = 102.89 g
Mass of KI = 0.3 mol KI * 166 g/mol = 49.8 g
Mass of KI = 0.3 mol KI * 1 mol I/1mol KI * 1 mol I₂/2 mol I * 253.81 g/mol = 38.07 g
Mass %I₂ = 38.07/(102.89+49.8) * 100 = 24.9%