$\begin{array}{l}
y = {x^3} - 6{x^2} + 3\left( {m + 2} \right)x - m - 6\\
\Rightarrow y' = 3{x^2} - 12x + 3\left( {m + 2} \right)\\
\Rightarrow y' = 0 \Leftrightarrow 3{x^2} - 12x + 3m + 6 = 0\\
\Leftrightarrow {x^2} - 4x + m + 2 = 0\,\,\,\,\left( * \right)\\
\Rightarrow ham\,\,so\,\,co\,2\,\,diem\,\,cuc\,\,\,tri\\
\Leftrightarrow \left( * \right)\,\,\,co\,\,\,hai\,\,\,nghiem\,\,pb \Leftrightarrow \Delta > 0\\
\Leftrightarrow 4 - m - 2 > 0 \Leftrightarrow m < 2.\\
Ta\,\,\,co:\,\,y = \left( {Ax + B} \right)y' + mx + n\\
\Rightarrow d:\,\,\,y = mx + n\,\,\,la\,\,duong\,\,thang\,\,di\,\,qua\,\,\,2\,\,diem\,\,cuc\,\,tri\,\,cua\,\,ham\,\,so.\\
\frac{y}{{y'}} = \frac{{{x^3} - 6{x^2} + 3\left( {m + 2} \right)x - m - 6}}{{3{x^2} - 12x + 3\left( {m + 2} \right)}}\\
\Rightarrow y = \left( {\frac{1}{3}x - \frac{2}{3}} \right)y' + 2\left( {m - 2} \right)x + m - 2.\\
\Rightarrow d:\,\,\,y = 2\left( {m - 2} \right)x + m - 2\,\,\,la\,\,duong\,\,thang\,\,di\,\,qu\,\,hai\,\,diem\,\,cuc\,\,\,tri\,\,cua\,ham\,\,so.
\end{array}$
