What is the interval of a for which the equation ||x-2|+a|=4 can have four distinct solutions for x?

There are two solutions or no solutions. If we take ‘a’ as positive then two solutions are for a < 4. Similarly two solutions when ‘a’ < -4.

There are two ways to solve the problem. Refer images for the same.

Long Answer

Short answer

Last line says : Similar results when a < -4.