((4*sqrt(5))/(2))-((3*sqrt(5))(2))

((4*sqrt(5))/(2))-((3*sqrt(5))(2)) =  

(1/2)[4*sqrt(5)] - (1/2)[3*sqrt(5)]  =      factor out the (1/2)

(1/2) [4sqrt(5) - 3sqrt(5)] =

(1/2)sqrt(5)  ...... or just..... sqrt(5)/2

CPhill:  His/her expression can be written like this:

1/2 (4 sqrt(5))-(3 sqrt(5))×2

After a number of reducing steps we get:

-4sqrt(5), which is the correct  answer. Good luck.