If there were a 1 mol quantity of #BaCO_3#, clearly there would be 3 mol of oxygen atoms present. The question specifies a 0.25 mol quantity of #BaCO_3#, so we have 0.75 mol oxygen atoms .
If we have 0.25 mol #BaCO_3#, clearly there are 0.25 mol Ba atoms, and 0.75 mol oxygen atoms, because for every mol of Ba, there must be 3 mol oxygen atoms, and 1 mol carbon. Please note that I quote the answer in oxygen atoms , and not oxygen molecules, i.e. #O_2# species.