To compare the expressions $|-4|$ and $-|-4|$, evaluate both sides separately. For the left side, the absolute value of $-4$ is $4$. For the right side, evaluate the absolute value first to get $4$, and then apply the external negative sign, resulting in $-4$. Comparing the two simplified integers on the number line, the positive value $4$ is greater than the negative value $-4$ ($4 > -4$). As a result, the correct relationship is $|-4| > -|-4|$. This comparison highlights the structural difference between an absolute value and its direct opposite.