How many ammonium ions and how many sulfate ions are present in an 0.260 mol sample of (nh4)2so4?

The question requires that you assume complete ionization of the compound. This is:

(NH4)2 SO4 → 2 NH4 (+) + SO4 (2-)

Then, 1 mol of (NH4)2 SO4 produces 3 moles of ions: 2 moles of NH4 (+) and 1 mol of SO4 (2-)

=> 0.26 * 2 moles of NH4(+) = 0.52 moles of NH4 (+)

0.26 * 1 mol of SO4 (2-) = 0.26 moles of SO4 (2-).

0.52 moles of ammonium ions and 0.26 moles of sulfate.ions.