The reason extraneous solutions exist is because some operations produce 'extra' answers, and sometimes, these operations are a part of the path to solving the problem. When we get these 'extra' answers, they usually don't work when we try to plug them back into the original problem.

Why do extraneous solutions occur?

​Extraneous Solutions occur because squaring both sides of a square root equation results in 2 solutions (the positive and negative number). Therefore, one of those numbers will be an extraneous solution, or an extra solution which does not fulfill the original equation.

Why are there extraneous solutions in absolute value equations?

Right from the start, you can say that any negative value of x will be an extraneous solution because the absolute value of a number can only be positive. This solution will be extraneous because it implies that the absolute values of 4 is negative, which is false.