First, rewrite the left side of the inequality as:

#-2 - 2x - 2 > 6#

#-2 - 2 - 2x > 6#

#-4 - 2x > 6#

Next, add #color(red)(4)# to each side of the inequality to isolate the #x# term while keeping the equation balanced:

#-4 + color(red)(4) - 2x > 6 + color(red)(4)#

#0 - 2x > 10#

#-2x > 10#

Now, divide each side of the inequality by #color(blue)(-2)# to solve for #x# while keeping the inequality balanced. However, because we are dividing an inequality by a negative number we must reverse the inequality operator:

#(-2x)/color(blue)(-2) color(red)(<) 10/color(blue)(-2)#

#(color(red)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(<) -5#

#x < -5#