f(x)=2 |x-2| ; f(-2), f(x^2+2)

f(-2) = 2|-2-2) = 2|4| = 2(4) = 8

f(x^2 + 2) = 2|x^2 + 2 - 2)|
= 2|x^2| = 2x^2

(x^2 is always positive anyway, so the |..| sign is redundant.