$a)$

$18x\ne 0\Rightarrow x\ne 0\Rightarrow D=\mathbb{R}\backslash \left\{0\right\}$

$\frac{72}{18x}=\frac{8}{2x}=\frac{4}{x}$

$x=\frac{1}{2}\Rightarrow \frac{4}{\frac{1}{2}}=4:\frac{1}{2}=4\cdot 2=8$

$x=-\frac{3}{2}\Rightarrow \frac{4}{-\frac{3}{2}}=4:\left(-\frac{3}{2}\right)=4\cdot \left(-\frac{2}{3}\right)=-\frac{8}{3}$

$b)$

$2x^2\ne 0\Rightarrow x^2\ne 0\Rightarrow x\ne 0\Rightarrow D=\mathbb{R}\backslash \left\{0\right\}$

$\frac{16x}{2x^2}=\frac{8}{x}$