$\begin{array}{l}{\text{Here, [(144)}}^{\text{2}}÷\text{48}\times \text{?]}÷\text{22 = 216}\\ \\ \text{We follow the BODMAS rule.}\\ \\ \Rightarrow [\frac{\text{144}\times \text{144}}{48}\times ?]÷22=216\\ \\ \Rightarrow (432\times ?)÷22=216\\ \\ \Rightarrow (432\times ?)=216\times 22\\ \\ \Rightarrow ?=\frac{216\times 22}{432}=11\end{array}$

Hence, Option C is correct.