I have no problem sketching the graph of |2x| or |X-a|. However, the problem I sometimes have is I miss out the intersections in my sketch. For example, in this question, my sketch only showed the intersection in the positive x - axis.
In my mind, I thought that the graph of would |2x| would increase a lot faster than |x-a|, so there would be no intersection in the negative x-axis.
If it makes you feel better, you can compute the intersection point. You're looking at the lines $y=-2x$ and $y=-x+a$ when $x<0$. They intersect when $$-2x=-x+a\Leftrightarrow x=-a$$ which is indeed a negative solution.