When an inequality is multiplied or divided by a negative number, the inequality symbol must be flipped. This has not been done in the last step. -4x<8x<-2 Ron-Jon divided both sides with -4 but he forgot to flip the sign.
Let's start from the beginning. Remember the rule for inequalities when multiplying or dividing by a negative.
The inequality is, therefore, true if x>-2. Ron-Jon's solutions should have been as follows.