Evaluate using the definition of absolute value |x-2|=6

Well, the definition of absolute value is distance from zero, so we're making a graph.

Make a number line where 0 is in the center. You know that the distance from 0 is 6, so put x-2 at the -6 and the 6 points. Now add two to both of those, and now graph on the -4 point "x₁", and on the 8 point "x₂". Put down x₁ = -4 and x₂ = 8 (the normal way, not on the graph) next to it, and you'll be done.