(b) How many moles of ammonium ions are in 0.417 g of ammonium carbonate

The formula of am. carbonate is (NH4)2 CO3 and its molar mass = 96
Moles of am carbonate in 0.417 g = (0.417) / 96 = 0.00434 moles.
Each mole of am. carbonate has 2 moles of ammonium ions
No. of moles of ammonium ions = 2 x 0.00434 = 0.00868