Using the answers possible, you could pick x=0 and see if 0 work.
-3 + | 0-2 | > 5
-3 + | -2 | > 5
-3 + 2 > 5
-1 > 5
this is false, so any answer that includes 0 is not correct
this eliminates "-6 < x < 10" and "x > -6 or x < 10" since they both include 0.
that leaves only "x < -6 or x > 10".
And the graph that matches this answer is the very bottom graph with two open circles at -6 and 10 and arrows pointing outward.
Now if you want to solve the inequality, that'd look like this:
-3 + | x - 2 | > 5
| x - 2 | > 8 by adding 3 to both sides
this will split into "x - 2 > 8 or x - 2 < -8"
Solving each of those, you'd have "x > 10 or x < -6" which is the answer we previously determined.