① When x ≤ 2, the analytic formula of piecewise function is: y = x+2,

Its image is "the part of parabola y = x+2 when independent variable x ≤ 2", as can be seen from the figure:

To make the function value y = 8, substitute y = 8 into y = x+2 and get: x = √ 6.

For the square of y = x +2, if the range of the independent variable is not limited, it is obvious that when the independent variable x = √ 6, the function value y = 8；; ; Now the topic requires "independent variable x ≤ 2", so the function value y = 8 only when independent variable x =-√ 6. (Because -√ 6 satisfies "independent variable x ≤ 2"; +√6 does not satisfy "independent variable x ≤ 2", so it is omitted)

That is, in this problem, due to the limitation of the original problem "independent variable x ≤ 2", X can't get √6 (because √ 6 > 2).

② When x > 2, the analytic formula of piecewise function is y = 2x, and its image is "the part of straight line y = 2x when independent variable x ≤ 2".

Substituting y = 8 into the analytical formula y = 2x, we get: x = 4. And x = 4 satisfies the requirement that the independent variable x > 2.

This shows that when the independent variable x = 4, the function value of the original piecewise function is 8.

To sum up, when the function value of the piecewise function is 8, the value of the corresponding independent variable X is: x = 4 or X =-√ 6.

So, the answer is D.

Good luck with your study!