The whole idea behind absolute value is to turn the value into positive no matter what the sign of the value is. x<0 and y>0 => |x|−|y| is positive x - positive y while |x−y| = |negative+negative| = positive x + positive y => B is greater.

Concept #1: If x < 0, then |x| = -x
For example: |-3| = -(-3) = 3
and |-11| = -(-11) = 11

Concept #2: If y > 0, then |y| = y
For example: |8| = 8
and |22| = 22

Concept #3: If x < 0 and y > 0 then x < 0 < y
This means x < y
So, if we subtract y from both sides, we get: x - y < 0
So, applying Concept #1, we can see that |x - y| = -(x - y)
Upon substitution, we get:

QUANTITY A: |x| - |y| = (-x) - y
QUANTITY B: -(x - y)

Simplify
QUANTITY A: -x - y
QUANTITY B: -x + y

Add x to both quantities to get:
QUANTITY A: -y
QUANTITY B: y

Add y to both quantities to get:
QUANTITY A: 0
QUANTITY B: 2y

Since y > 0, we know that 2y > 0

Answer: B

Cheers,
Brent

x<0 and y>0
case 1 -
if x=-1 and y=2
|x|−|y|=1-2=-1
|x-y|=1 where B is greater
case 2 -
if x=-1 and y=4
|x|-|y|=-5
|x-y|=5
where B is greater
So, answer is B

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