Question

What value or values for x make the following inequality true?

Answer 1

$|x-3|=13\\ x-3=13\vee x-3=-13\\ x=16 \vee x=-10$

So, it's B.

Answer 2

To answer this question, you must first learn what the absolute value sign 
(|    |)  does. It makes the product positive. For example,  if you have |7-10| that would be -3, but because of the absolute value it is now just 3.
Checking answers:
|11-3|=13    = |8| which is 8 and not equal to 13
|-10-3|=13   = |-13| which is 13 and is equal
|-15-3|=13   = |-18| which is 18 and not equal
|15-3|=13    = |12| which is 12 and not equal
Answer is B