Solution: According to the meaning of the question, A (-2,0), B (0 0,4),

The two points passing through C and D are the vertical lines of X axis and Y axis respectively, and the two vertical lines intersect at E point.

From the nature of rotation, it can be known that △ CDE △ BOA, then DE=OA=2, CE=OB=4.

Let C(x, kx) and D(x+2, kx+2) be on the image of inverse proportional function y=yx.

According to the meaning of the question, x+2=3x and the solution is x= 1.

∴C( 1,k),D(3,k3)，

CE = 4，

∴k-k3=4, and the answer is k = 6.

So choose D.