If $$\left(4x + 2y\right) 3 + \left(4x - 2y\right) 3 = 16 \left(Ax^{3} + Bxy^{2}\right)$$, then what is the value of $$\frac{1}{2}\left(\sqrt{A^{2} + B^{2}}\right)$$?

A

8

B

3

C

5

D

7