Answer
See below.
Work Step by Step
For any real numbers $x$ and $y$, we only need to consider three cases:
Case1: both are positive, we have $LHS=|x|\cdot |y|=xy=|xy|=RHS$;
Case2: both are negative, we have $LHS=|x|\cdot |y|=(-x)(-y)=xy=|xy|=RHS$;
Case3: they have oppsit signs, we have $LHS=|x|\cdot |y|=-xy=|xy|=RHS$;
thus in any case, the statement is true.