For expressions like ||x-1|-2|=1: work from inside out. Let u=|x-1|, then |u-2|=1 gives u=1 or u=3. Then |x-1|=1 gives x=0,2 and |x-1|=3 gives x=-2,4. Total 4 solutions. Always peel one layer at a time. Check that intermediate variable constraints (like u>=0) are satisfied.