We've got to find a set of points (x,y) (and mark it on a plane) which satisfies this inequality.That's all.
Well then you have included that.
You know that $\displaystyle x>0~\&~x\ne 1$, WHY?
For the same reason $\displaystyle y\ne 2$.
If $\displaystyle y>e+2$ then $\displaystyle \log_x|y-2|>0$ WHY?
What about $\displaystyle y<2-e~?$