The answer is $\boxed{10}$.
In the proportion $8:24::?:32$, the two inner terms are in the ratio $2:3$. This means that the two outer terms must also be in the ratio $2:3$. Therefore, the missing term is $10$, which is $2$ times $8$ and $3$ times $8$.
Option A, $5$, is incorrect because it is not in the ratio $2:3$ with $8$ and $24$.
Option B, $6$, is incorrect because it is not in the ratio $2:3$ with $8$ and $24$.
Option C, $10$, is correct because it is in the ratio $2:3$ with $8$ and $24$.
Option D, $8$, is incorrect because it is not in the ratio $2:3$ with $8$ and $24$.
