Answer
$$\beta =\frac{3}{2}.$$
Work Step by Step
$ w $ is parallel to $ v $ if and only if $ w=mv $, that is, $$ w=mv\Longrightarrow \langle-2,\beta \rangle=m\langle4,-3 \rangle.$$
Hence, we get
$$-2=4m, \quad \beta=-3m\Longrightarrow m=-\frac{1}{2}, \quad \beta =\frac{3}{2}.$$
