2. Given the complex numbers $z_{1}=m+2 \mathrm{i}, z_{2}=3-4 \mathrm{i}$. If $\frac{z_{1}}{z_{2}}$ is a real number, then the value of the real number $m$ is ( ).
(A) $\frac{8}{3}$
(B) $\frac{3}{2}$
(C) $-\frac{8}{3}$
(D) $-\frac{3}{2}$
2. D.

Notice that
$$
\frac{z_{1}}{z_{2}}=\frac{m+2 \mathrm{i}}{3-4 \mathrm{i}}=\frac{(3 m-8)+(6+4 m) \mathrm{i}}{25} \text {. }
$$

Thus, $6+4 m=0 \Rightarrow m=-\frac{3}{2}$.