B and M are incorrect. Can you recheck those and see what the problem is?
Also, the graph is a bit unclear as x -> 4... is that supposed to be an asymptote, or do the curves actually stop at ? If theres an asymptote, the one sided limits will be , the regular two-sided limit won't exist. But I think that's an asymptote, so F and G are wrong too.
To answer your question, a one sided limit will exist if the function approaches a particular value (or to infinity), and gets arbitrarily close as you get closer and closer, FROM that direction.
The usual two-sided limit will exist ONLY if the left-hand and right-hand limits exist and are equal.
The function will be continuous if the limit exists, AND the limit actually equals the function value. Notice that this does actually happen at x=6.
Edit: A looks incorrect as well.