Chapter 2 - Section 2.1 - Introduction to Integers - Exercise Set - Page 105: 73

$-|-12|\lt -(-12)$

If $a-b \lt 0$, then $a \lt b;$ If $a-b \gt 0$, then $a \gt b;$ If $a-b = 0$, then $a=b;$ In this problem, $a=-|-12|=-12,$ $b=-(-12)=12,$ Since $a-b=-12-12=-24\lt0,$ Then $a\lt b,$ Therefore, $-|-12|\lt -(-12)$