\(8^{2x}.64^2=16^{x+4}\)
\(\left(2^3\right)^{2x}.\left(2^6\right)^2=\left(2^4\right)^{x+4}\)
\(2^{6x}.2^{12}=2^{4x+16}\)
\(2^{4x+16}:2^{6x}=2^{12}\)
\(2^{4x+16-6x}=2^{12}\)
\(2^{-2x+16}=2^{12}\)
\(\Rightarrow-2x+16=12\)
\(\Rightarrow2x=4\Rightarrow x=2\)