The only thing this is really asking you to do is to understand subscripts and parentheses.
Examining #("NO"_3)_2# only, we see that the subscript #3# indicates #\mathbf(3)# #\mathbf("mol")#s of oxygen atoms within each #"mol"# of #"NO"_3^(-)# (nitrate) polyatomic ions.
The subscript #2# indicates #\mathbf(2)# #\mathbf("mol")#s of #"NO"_3^(-)# polyatomic ions. As a result, we double the number of oxygens as well as the number of nitrogens (but we only care about the oxygens here) that we already have.
Thus, #("O"xx3)xx2 = \mathbf6# moles of oxygen atoms.