Answer
$$\left( {4, - \frac{\pi }{4},4} \right)$$
Work Step by Step
$$\eqalign{
& \left( {2\sqrt 2 , - 2\sqrt 2 ,4} \right) \cr
& \left( {x,y,z} \right):{\text{ }}\left( {2\sqrt 2 , - 2\sqrt 2 ,4} \right) \to x = 2\sqrt 2 ,{\text{ }}y = - 2\sqrt 2 ,{\text{ }}z = 4 \cr
& {\text{Rectangular to cylindrical}} \cr
& {r^2} = {x^2} + {y^2} \to r = \sqrt {{{\left( {2\sqrt 2 } \right)}^2} + {{\left( { - 2\sqrt 2 } \right)}^2}} = 4 \cr
& \tan \theta = \frac{y}{x} \to \theta = {\tan ^{ - 1}}\left( {\frac{{ - 2\sqrt 2 }}{{2\sqrt 2 }}} \right) = - \frac{\pi }{4} \cr
& z = z \to z = 4 \cr
& {\text{The cylindrical coordinates are:}} \cr
& \left( {4, - \frac{\pi }{4},4} \right) \cr} $$
