Pretend that your #<=# here is just a plain old #=#. Balance it like you always would :)
#4x+8<=6x-20# Subtract #6x# from both sides
#-2x+8<=-20# Subtract #8# from both sides
#-2x<=-28# Divide both sides by #-2# and do not forget to flip the sign because you're dividing by a negative number!
#x >= 14#