Đáp án:
$\begin{array}{l}
a)mx - 2x + 3 = 0\\
\Leftrightarrow \left( {m - 2} \right)x = - 3\\
Thay\,m = - 4\\
\Rightarrow - 6x = - 3\\
\Rightarrow x = \frac{1}{2}\\
Vậy\,x = \frac{1}{2}\,khi\,m = - 4\\
b)x = 2\\
\Rightarrow \left( {m - 2} \right).2 = - 3\\
\Rightarrow m - 2 = \frac{{ - 3}}{2}\\
\Rightarrow m = \frac{1}{2}\\
c)\left( {m - 2} \right)x = - 3\,
\end{array}$
Để pt có nghiệm duy nhất thì: $m - 2 \ne 0 \Rightarrow m \ne 2$
d)
$\begin{array}{l}
m \ne 2\\
\Rightarrow x = \frac{{ - 3}}{{m - 2}} \in Z\\
\Rightarrow - 3 \vdots \left( {m - 2} \right)\\
\Rightarrow \left( {m - 2} \right) \in \left\{ { - 3; - 1;1;3} \right\}\\
\Rightarrow m \in \left\{ { - 1;1;3;5} \right\}
\end{array}$
Vậy $m \in \left\{ { - 1;1;3;5} \right\}$
