the first part of the solution finds C
by using the property that the integral on the density function equals 1

the problem starts in the second part of the question
i need to find the distribution function of Y
where Y=||x|-1|
(my problem i written bellow the photo)

for y<0 we have no graph so the probability is 0.
but when its from zero to 1 it touches four points
i dont know how they got the integral from that fact?
the same goes for when y>1
what is the logic?