What are the solutions of the following equation? 5∣x+6∣+8=-6∣x+6∣+8

So think of |x+6| as a single object. Move the - 6|x+6| to the left side and move the 8 to the right side to get 11|x+6| = 0. Then divide both sides by 11 to get |x+6| = 0 and in this instance the || can be dropped because + 0 and - 0 are the same. so x + 6 = 0 or x=-6