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\(2^x\cdot\left(-2\right)^{2x}\cdot8^x=4^6\)
\(\Leftrightarrow2^x\cdot2^{2x}\cdot\left(2^3\right)^x=\left(2^2\right)^6\)
\(\Leftrightarrow2^{x+2x+3x}=2^{12}\)
\(\Rightarrow x+2x+3x=12\)
\(\Rightarrow x=2\)