Có bao nhiêu giá trị nguyên của tham số $m$ thuộc đoạn $\left[...

$\Leftrightarrow \left( {{2}^{m}}-{{2}^{2x}} \right)\left( {{2}^{m}}+{{2}^{2x}}-{{4.2}^{x}} \right)>0\Leftrightarrow \left[ \begin{aligned}
& \left\{ \begin{aligned}
& {{2}^{m}}>{{2}^{2x}} \\
& {{2}^{m}}>{{4.2}^{x}}-{{2}^{2x}} \\
\end{aligned} \right.\left( 1 \right) \\
& \left\{ \begin{aligned}
& {{2}^{m}}<{{2}^{2x}} \\
& {{2}^{m}}<{{4.2}^{x}}-{{2}^{2x}} \\
\end{aligned} \right.\left( 2 \right) \\
\end{aligned} \right.$$\forall x\in \left( -\infty ;4 \right]\Rightarrow \left\{ \begin{aligned}
& 0<{{2}^{2x}}\le {{2}^{8}} \\
& -192\le {{4.2}^{x}}-{{2}^{2x}}\le {{2}^{2}} \\
\end{aligned} \right..\left\{ \begin{aligned}
& {{2}^{m}}>{{2}^{2x}} \\
& {{2}^{m}}>{{4.2}^{x}}-{{2}^{2x}} \\
\end{aligned} \right.\forall x\in \left( -\infty ;4 \right]\Leftrightarrow \left\{ \begin{aligned}
& {{2}^{m}}>{{2}^{8}} \\
& {{2}^{m}}>{{2}^{2}} \\
\end{aligned} \right.\Leftrightarrow m>8m\left[ -2023;2023 \right]2015m\left\{ \begin{aligned}
& {{2}^{m}}<{{2}^{2x}} \\
& {{2}^{m}}<{{4.2}^{x}}-{{2}^{2x}} \\
\end{aligned} \right.\forall x\in \left( -\infty ;4 \right]\Leftrightarrow \left\{ \begin{aligned}
& {{2}^{m}}\le 0 \\
& {{2}^{m}}<-192 \\
\end{aligned} \right. m2015m$.