Haha, this is from a STAV paper, right?
Is the mass supposed to be 8.2? I'm just guessing it is because there's a dot after the eight and it would give us nicer numbers.
So we have 0.1 mol of this hydrocarbon. Lets look at the products of the reaction:
16.2g of HBr, or approximately 0.2 mol. How do we form HBr? Through a substitution reaction between bromine and a hydrogen atom on the hydrocarbon. Each substitution reaction adds one bromine to the hydrocarbon and forms one molecule of HBr. There is 0.2 mol of HBr and 0.1 mol of the hydrocarbon, so there have been two substitution reactions on each hydrocarbon, each adding one bromine atom. Hence, 2 atoms of bromine per hydrocarbon molecule.
We also have 12g of Br2 in excess, which means that 48g of bromine has reacted, which is 0.3 mol of bromine. Now, 0.2 mol of that bromine went to producing HBr, which means that we still have 0.1 mol of bromine unreacted. Where does this go? Addition reaction! Chemistry is exciting. So we have 0.1 mol of bromine undergoing an addition reaction with 0.1 mol of the hydrocarbon, which means each hydrocarbon is undergoing one addition reaction. Each addition reaction adds to bromine atoms to the hydrocarbon, so the answer is again, 2 bromine atoms per hydrocarbon molecule.