ĐK: $x>0$.
Đặt: $t=\log_2x \Rightarrow x=2^t$
Phương trình đã cho trở thành:
$4^{t+1}-(2^t)^{\log_26}=2.3^{2t+2}$
$\Leftrightarrow 4^{t+1}-(2^{\log_26})^t=18.9^t$
$\Leftrightarrow 4^t=18.9^t+6^t$
$\Leftrightarrow 18.\left(\dfrac{9}{4}\right)^t+\left(\dfrac{6}{4}\right)^t=4$
$\Leftrightarrow 18.\left(\dfrac{3}{2}\right)^{2t}+\left(\dfrac{3}{2}\right)^t-4=0$
$\Leftrightarrow \left(\dfrac{3}{2}\right)^t=\dfrac{4}{9}$
$\Leftrightarrow t=-2 \Leftrightarrow x=\dfrac{1}{4}$