Al³⁺ has a lower ionic radius than Mg²⁺ ion because

As we can see  here that both the species are isoelectronic species,as they all contain the same number of electrons i.e,10.

And we know that for  isoelectronic species size depends upon the effective nuclear charge, more  is the positive charge,more is the effective nuclear charge and thus ,lesser is the size.

Hence,${\mathrm{Al}}^{3+}$ has a lower ionic radius than ${\mathrm{Mg}}^{2+}$ ion because it  has a higher nuclear charge than ${\mathrm{Mg}}^{2+}$.

Hence, option(b) is correct.