The trick here is to realize that the nitride anion,
In other words, the nitride anion has the same number of electrons as neon.
As you know, one mole of any element is defined as
#color(blue)(|bar(ul(color(white)(a/a)"1 mole" = 6.022 * 10^(23)color(white)(a)"atoms"color(white)(a/a)|))) ->#Avogadro's number
In your case, one mole of nitride anions will contain
#6.022 * 10^(23) color(red)(cancel(color(black)("N"^(3-)"ions"))) * "8 valence e"^(-)/(1color(red)(cancel(color(black)("N"^(3-)"ion")))) = color(green)(|bar(ul(color(white)(a/a)color(black)(4.8 * 10^(24)color(white)(a)"valence e"^(-))color(white)(a/a)|)))#
I'll leave the answer rounded to two sig figs.
SIDE NOTE It's worth mentioning that this problem is aimed at testing your knowledge of valence electrons and of Avogadro's number; this problem is not very practical because the nitride anion cannot exist in solution.
That is the case because it acts as a base in aqueous solution, i.e. it gets protonated by water.