If oxide ions are arranged in hcp and the aluminium ions occupy two thirds of octahedral voids. What will be the formula of the compound?

The correct option is B $A{l}_2{O}_3$
In $hcp$ arrangement of oxide ion :

Number of octahedral (oh) voids for each oxide ion $=1$

Number of tetrahedral (Td) voids for each oxide ion $=2$

$A{l}^{3+}$ occupies only 2/3 of octahedral voids.

Thus, number of $A{l}^{3+}$ for each oxide ion $=2/3$

$\Rightarrow$ Ratio of oxide ion : Aluminium ion

$\Rightarrow 3:2$

Thus, formula is $A{l}_2{O}_3$.

Hence the correct option is B.