I gather that the way in which you meant to write the question was (x-2)2=-8.
If so, I think the easiest way to solve this is to take the +/- square root of both sides to obtain that x-2=±2i√2.
We can then solve for x to obtain x=2±2i√2.
Alternatively, (and I do not recommend this, although it may be useful in general if the root did not have a multiplicity...for instance (x-2)(x-3)=2, in which the factors are distinct), you can expand the left hand side and re-write the equation as standard
form of a parabola equated to 0, and then solve for the roots.
In this problem, that would play out as: x2-4x+4=-8 ---> x2-4x+12=0. Using the quadratic formula, we get x=2±2i√2, exactly as obtained before.
Hope this helps.