We're asked to find the mass, in #"g"#, of oxygen in #6.15xx10^23# #"formula units (NH"_4")"_2"SO"_4#.
To do this, we recognize that there are #4# #"atoms O"# per formula unit of ammonium sulfate:
#6.15xx10^23cancel("formula units (NH"_4")"_2"SO"_4)((4color(white)(l)"atoms O")/(1cancel("formula unit (NH"_4")"_2"SO"_4)))#
#= 2.46xx10^24# #"atoms O"#
Now, we use Avogadro's number to find the number of moles of #"O"#:
#2.46xx10^24cancel("atoms O")((1color(white)(l)"mol O")/(6.022xx10^23cancel("atoms O"))) = ul(4.085color(white)(l)"mol O"#
Finally, we use the molar mass of oxygen (#15.999# #"g/mol"#) to convert from moles to grams:
#4.085cancel("mol O")((15.999color(white)(l)"g O")/(1cancel("mol O"))) = color(red)(ul(65.4color(white)(l)"g O"#
