CONCEPTS: The question tests on the area of functions.

SOLUTION:
f(a+2) = (a+2)^2 + 3(a+2) -4
= a^2 +4 +4a + 3a +6 - 4
= a^2 +7a +6 (OPTION A)

Alternatively if a=0
f(a+2)= f(0+2) =f(2)=2^2+ 3.2- 4
=6 (You can see option A&E gives 6 as answer if a=0)
With a negative number like a=-1
f(2+a)= f(2-1)=f(1)
=1^2+3-4
=0 (You can see option A gives 0 as answer and E gives 8 as answer;Eliminate E)
 Hence OPTION (A)