$\begin{array}{l}\text{ Here}\\ \Rightarrow \text{ (4}\times {\text{4)}}^{\text{3}}÷(\text{(512}÷{\text{8)}}^{\text{4}}\times \text{(32}\times {\text{8)}}^{\text{4}})\text{=(2}\times {{\text{2)}}^{?}}^{\text{+4}}\\ \\ \Rightarrow {\text{ (16)}}^{\text{3}}÷{\text{(64)}}^{\text{4}}\times {\text{(256)}}^{\text{4}}{{\text{= (4)}}^{\text{?}}}^{\text{+4}}\\ \\ \Rightarrow {\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}(4)}}^{\text{2}\times \text{3}}÷{\left({\text{4}}^{\text{4}}\right)}^{\text{4}}\times {\left({\text{4}}^{\text{5}}\right)}^{\text{4}}{{\text{= (4)}}^{\text{?}}}^{\text{+4}}\\ \\ \Rightarrow {{\text{ 4}}^{\text{6}}}^{\text{-16}}{{\text{+20 = (4)}}^{\text{?}}}^{\text{+4}}\\ \\ \Rightarrow \text{\hspace{0.17em}\hspace{0.17em}?+4=10}\\ \\ \Rightarrow \text{\hspace{0.17em}\hspace{0.17em}?=6}\end{array}$

Hence, Option C is correct.