Find all $a$ such that $\sqrt {(a+2)^2} + \sqrt {(a-2)^2} = 4$

We can rewrite this as

l a + 2  l  +  l a - 2 l   = 4

Solving this graphicaly  where a   =  x    ⇒  https://www.desmos.com/calculator/rxwvtu2txd

The solution is that     a  =  [ -2, 2 ]