First, add #color(red)(6)# to each side of the inequality to isolate the #z# term while keeping the inequality balanced:
#z/-2 - 6 + color(red)(6) <= -2 + color(red)(6)#
#z/-2 - 0 <= 4#
#z/-2 <= 4#
Now, multiply each side of the inequality by #color(blue)(-2)# to solve for #z# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:
#color(blue)(-2) xx z/-2 color(red)(>=) color(blue)(-2) xx 4#
#cancel(color(blue)(-2)) xx z/color(blue)(cancel(color(black)(-2))) color(red)(>=) -8#
#z >= -8#
