Plz help! serious answers only

I’ve been trying all day to figure this puzzle out. i need the work for it aswell. it is a factoring polynomials tarsia. the image is below.

Suppose the equation ||x-a|-b|=2008 has 3 distinct real roots and a not =0. find the value of b.

Monthly water bills for a city have a mean of $108.43 and a standard deviation of $36.98. find the probability that a randomly selected bill will have an amount greater than $173, which the city believes might indicate that someone is wasting water. would a bill that size be considered unusual?