When the graph of the function $y = 2 ^ { x } + 2$ is translated in the $x$-direction by $m$ units, and this graph is symmetric to the graph of the function $y = \log _ { 2 } 8 x$ translated in the $x$-direction by 2 units with respect to the line $y = x$, what is the value of the constant $m$? [3 points]\\
(1) 1\\
(2) 2\\
(3) 3\\
(4) 4\\
(5) 5