Chọn phương án C.

Đặt \(t=\left(\dfrac{4}{3}\right)^x\;(t>0)\), ta có $$\begin{aligned}
&\,64\cdot9^x-84\cdot12^x+27\cdot16^x<0\\
\Leftrightarrow&\,64-84\cdot\dfrac{12^x}{9^x}+27\cdot\dfrac{16^x}{9^x}<0\\
\Leftrightarrow&\,64-84\cdot\left(\dfrac{12}{9}\right)^x+27\cdot\left(\dfrac{16}{9}\right)^x<0\\
\Leftrightarrow&\,64-84\cdot\left(\dfrac{4}{3}\right)^x+27\cdot\left(\dfrac{4}{3}\right)^{2x}<0\\
\Leftrightarrow&\,27\cdot\left[\left(\dfrac{4}{3}\right)^x\right]^2-84\cdot\left(\dfrac{4}{3}\right)^x+64<0\\
\Leftrightarrow&\,27t^2-84t+64<0
\end{aligned}$$

Suy ra $$\begin{aligned}
\begin{cases}
t>\dfrac{4}{3}\\
t<\dfrac{16}{9}
\end{cases}\Leftrightarrow&\begin{cases}
\left(\dfrac{4}{3}\right)^x>\dfrac{4}{3}\\
\left(\dfrac{4}{3}\right)^x<\dfrac{16}{9}
\end{cases}\\
\Leftrightarrow&\begin{cases}
x>1\\
x<2.
\end{cases}
\end{aligned}$$