Point d is the midpoint of line segment OB,

∴ The coordinate of point B is (2x, 2y);

∫△OBC has an area of 4,

∴12×××| 2x×××| 2y | = 4, that is |xy|=2.

Point b is located in the second quadrant,

∴k=-|xy|=-2；

Point e is on the hyperbola y = kx,

∴ The coordinate of point E is (2x,1x);

∴ce:be= 1x:(2y- 1x)= 1x:(2×2x- 1x)= 1:3；

So choose B.