$a)$  

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

$\frac{{\sout{14}}^2}{x+2}\cdot \frac{x^2-4}{{\sout{7}}^1}=\frac{2}{\sout{x+2}}\cdot \sout{\left(x+2\right)}\cdot \left(x-2\right)=2\left(x-2\right)=2x-4$  

$b)$  

$x^2-16\ne 0\Rightarrow x^2\ne 16\Rightarrow \left(x\ne -4\wedge x\ne 4\right)\Rightarrow D=\mathbb{R}\backslash \left\{-4,4\right\}$