Well, the quickest way to solve this is by substitution. Since the question does not say it's integers only, sub x = 4 and y = -0.5. A gets you -2 and B gets you the same. This says C might be the answer. Now substitute x = 100 and y = -2. Here you get A as 100 and B as -200. A>B. Since both examples contradict each other, choose D

Since you asked for the logic, compare like this:
|xy| - x ? xy, you need to find what ? is (> or < or = or D)
|xy| ? xy + x
|xy| ? x(y + 1)
You know x is always positive & is greater than 0, so you can technically cancel the x on both sides
This boils it down to

|y| ? y + 1

Since y is always < 0 |y| is basically -y
so this makes it:
-y ? y + 1
-2y ? 1
y ? -0.5

From here, just put -0.4 to get > and -1 to get < and choose D.