Prove the statement: For all real numbers x and y, |x|.|y| = |xy|?

Actually, I'd also consider the cases where x=0 or y=0, so we'd also want to show the cases like: |0|*|y| = |0*y|

In any case, let's worry about the four cases:
x and y are positive:
|+| * |+| =? |+ * +|
+ * + = +

x is positive and y is negative:
|+| * |-| =? |+ * -|
+ * + =? |-|
+ * + = +

x is negative and y is positive.
Same as above but just reversed for x and y:

x and y are both negative:
|-| * |-| =? |- * -|
+ * + = |+|
+ * + = +