Solution:

We know $$\sqrt{\left(3-2\sqrt{3}\right)^2}+\sqrt{\left(3+2\sqrt{3}\right)^2 }$$ $$= |3-2\sqrt{3}| + |3+2\sqrt{3}|.$$ Since $3 < 2 \sqrt 3,$ we know that $3-2\sqrt{3} < 0.$

Therefore, our desired equation expression is equal to $$-3+2\sqrt{3} + 3+2\sqrt{3}$$$$= 4 \sqrt 3.$$

Thus, the correct answer is D .