Answer:
[tex]{ \tt{ \frac{8}{ {b}^{2} - 4} . \frac{b - 2}{2b + 4} \div \frac{4}{2 {(b + 2)}^{2} } }} \\ \\ = { \tt{ \frac{8}{(b - 2)(b + 2)} \times \frac{b - 2}{2b + 4} \div \frac{4}{2 {(b + 2)}^{2} } }} \\ \\ = { \tt{ \frac{8}{b + 2} \times \frac{1}{2b + 4} \times \frac{2(b + 2) {}^{2} }{4} }} \\ \\ = { \tt{ \frac{8}{2b + 4} \times \frac{2b + 4}{4} }} \\ \\ = { \tt{ \frac{8}{4} }} \\ \\ = { \underline{ \tt{ \: 2 \: }}}[/tex]
