You should always know space group of zinc blende (F-43m), positions of atoms (or ions) in the unit cell) and number of stoichiometric units in the unit cell (Z=4). From these data you can, in fact, calculate the Avogadro number. Sulfur anions occupy vertices of cube and the centers of each face. From geometry you can find the diagonal of face is equal to 4 radii of the sulfur anion. Edge of cube (a) can be calculated from equation:
a2+a2=(4R)2 (isosceles right triangle)
and volume of the unit cell is, of course:
V=a3 in pm3 (cube)
Dividing 4xMM of ZnS by its density you can calculate the volume of the Avogado number od unit cells in cm3. Finally, converting this number to pm3 and dividing it by the volume of the unit cell you can obtain the needed Avogadro number.