Đáp án:
$\begin{array}{l}
\left\{ \begin{array}{l}
d:y = \left( {m + 1} \right)x + n\left( {m \ne - 1} \right)\\
{d_1}:y = \left( {2m + 4} \right)x + 2n - 2\left( {m \ne - 2} \right)
\end{array} \right.\\
a)d//{d_1}\\
\Leftrightarrow \left\{ \begin{array}{l}
m + 1 = 2m + 4\\
n \ne 2n - 2
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m = - 3\\
n \ne 2
\end{array} \right.\\
Vậy\,m = - 3;n \ne 2\\
b)d \cap {d_1} \ne \emptyset \\
\Leftrightarrow m + 1 \ne 2m + 4\\
\Leftrightarrow m \ne - 3\\
Vậy\,m \ne - 3
\end{array}$