P' is the point of intersection of the line y=x and the line of slope 2 that passes through P.

[Sol] Letting (a,b) and (x',y') be the coordinates of P and P', respectively,

Calculating the equation of the line of slope 2 that passes through P.

y-b=2(x-a)

y=2x-2a+b

Since the lines y=x and y=2x-2a+b intersect at P'(x',y'),

x'=2a-b

y'=2a-b (That's my problem, how do you get x' and y'?)