Concept:Substitute x with x+2 and x−2 in the given function, then simplify.Explanation:Given f(x)=2x−x2.First, find f(x+2): replace x by x+2: f(x+2)=2(x+2)−(x+2)2.Next, find f(x−2): replace x by x−2: f(x−2)=2(x−2)−(x−2)2.Add them: f(x+2)+f(x−2)=[2(x+2)−(x+2)2]+[2(x−2)−(x−2)2].Now substitute x=0: f(2)+f(−2)=[2(0+2)−(0+2)2]+[2(0−2)−(0−2)2].Compute each term: 2(2)=4, (2)2=4 so first bracket: 4−4=0.Second: 2(−2)=−4, (−2)2=4 so second bracket: −4−4=−8.Add the results: 0+(−8)=−8.Answer:−8 (Option A).