Có bao nhiêu số thực $m$ để hàm số $y=\left|...

Đặt $f\left( x \right)=3{{x}^{4}}-4{{x}^{3}}-12{{x}^{2}}+m$ . Ta có $f'\left( x \right)=12{{x}^{3}}-12{{x}^{2}}-24x=0\Leftrightarrow \left[ \begin{aligned}
& x=0 \\
& x=-1 \\
& x=2 \\
\end{aligned} \right.$.
$f\left( -3 \right)=243+m$, $f\left( -1 \right)=-5+m$, $f\left( 0 \right)=m$, $f\left( 2 \right)=-32+m$ .
Khi đó $\left\{ \begin{aligned}
& A=\underset{\left[ -3;2 \right]}{\mathop{\max }} f\left( x \right)=\max \left\{ f\left( -3 \right);f\left( -1 \right);f\left( 0 \right);f\left( 2 \right) \right\} \\
& a=\underset{\left[ -3;2 \right]}{\mathop{\min }} f\left( x \right)=\min \left\{ f\left( -3 \right);f\left( -1 \right);f\left( 0 \right);f\left( 2 \right) \right\} \\
\end{aligned} \right.\Rightarrow \left\{ \begin{aligned}
& A=f\left( -3 \right)=243+m \\
& a=f\left( 2 \right)=-32+m \\
\end{aligned} \right..$
Vậy $\underset{\left[ -3;2 \right]}{\mathop{\max }} y=\max \left\{ \left| m+243 \right|;\left| m-32 \right| \right\}=150$
$\Leftrightarrow \left[ \begin{aligned}
& \left\{ \begin{aligned}
& \left| m+243 \right|=150 \\
& \left| m+243 \right|\ge \left| m-32 \right| \\
\end{aligned} \right. \\
& \left\{ \begin{aligned}
& \left| m-32 \right|=150 \\
& \left| m-32 \right|\ge \left| m+243 \right| \\
\end{aligned} \right. \\
\end{aligned} \right.\Leftrightarrow \left[ \begin{aligned}
& \left\{ \begin{aligned}
& \left[ \begin{aligned}
& m+243=150 \\
& m+243=-150 \\
\end{aligned} \right. \\
& 150\ge \left| m-32 \right| \\
\end{aligned} \right. \\
& \left\{ \begin{aligned}
& \left[ \begin{aligned}
& m-32=150 \\
& m-32=-150 \\
\end{aligned} \right. \\
& 150\ge \left| m+243 \right| \\
\end{aligned} \right. \\
\end{aligned} \right.\Leftrightarrow \left[ \begin{aligned}
& \left\{ \begin{aligned}
& \left[ \begin{aligned}
& m=-93(TM) \\
& m=-393(L) \\
\end{aligned} \right. \\
& -118\le m\le 182 \\
\end{aligned} \right. \\
& \left\{ \begin{aligned}
& \left[ \begin{aligned}
& m=182(L) \\
& m=-118(TM) \\
\end{aligned} \right. \\
& -393\le m\le -93 \\
\end{aligned} \right. \\
\end{aligned} \right.$
Do đó có hai giá trị của $m$ thỏa mãn yêu cầu bài toán.