If the unit cell of a mineral has cubic close packed (ccp) array of...

In ccp, ${O}^{2 -}$ ions are 4.
Hence total negative charge = -8
Let $A{l}^{3 +}$ ions be x, and $M{g}^{2 +}$ ions be y.
Total positive charge = 3x + 2y
$⇒ 3x + 2y = 8$
This relation is satisfied only by x = 2 and y = 1.
Hence number of $A{l}^{3 +} = 2$
and number of $M{g}^{2 +} = 1$
$⇒$ n = fraction of octahedral holes occupied by $A{l}^{3 +}$
$= \dfrac{2}{4} = \dfrac{1}{2}$
and m = fraction of tetrahedral holes occupied by $M{g}^{2 +}$
$= \dfrac{1}{8}$