To accurately compare the expressions $-(-15)$ and $-|-15|$, evaluate each mathematical notation separately. The expression on the left, $-(-15)$, dictates taking the opposite of the negative integer $-15$, which simplifies directly to the positive integer $15$. On the right side, evaluate the absolute value $|-15|$ first to get $15$, then apply the external negative sign to obtain $-15$. Comparing the two simplified integers reveals that the positive value $15$ is significantly greater than the negative value $-15$ ($15 > -15$). Consequently, the final established relationship is $-(-15) > -|-15|$.