#### Answer

$x_{1}=0;x_{2}=-6$

#### Work Step by Step

$\log _{8}\left( x+2\right) +\log _{8}\left( x+4\right) =\log _{8}8\Rightarrow \log _{8}\left( \left( x+2\right) \left( x+4\right) \right) =\log _{8}8$
$\Rightarrow x^{2}+6x+8=8\Rightarrow x^{2}+6x=0\Rightarrow x_{1}=0;x_{2}=-6$