Question 95091
if f(x)=x^2-2, 
then 
f(x+2)=(x+2)^2-2

.

putting it all together
f(x+2)-f(x)= (x-2)^2-2-(x^2-2) [multiply]
{{{(x^2+4x+4-2)-(x^2-2))}}}
{{{(x^2+4x+4-2-x^2-2)}}} [combine like-terms]
4x+4