Concept:Absolute value functions need to be split into piecewise forms based on the sign of x.Explanation:For x≥0, ∣x∣=x, so f(x)=2x−x=x and g(x)=2x+x=3x.For x<0, ∣x∣=−x, so f(x)=2x−(−x)=3x and g(x)=2x+(−x)=x.Now compute the composite values.(f∘g)(2): g(2)=3(2)=6, then f(6)=6, so (f∘g)(2)=6.(g∘f)(2): f(2)=2, then g(2)=6, so (g∘f)(2)=6.(g∘f)(−2): f(−2)=3(−2)=−6, then g(−6)=−6, so (g∘f)(−2)=−6.(f∘g)(−2): g(−2)=−2, then f(−2)=3(−2)=−6, so (f∘g)(−2)=−6.Check option D: (g∘f)(2)+(g∘f)(−2)=6+(−6)=0.Thus option D is correct.Answer:Option D.