1) Three boxes are kept between the boxes that contain Green and Red colour and either of them is at the top.

2) Four boxes are kept between the boxes that contain Pink and Orange colour.
3) The box that contains Orange colour is kept immediately below the box that contains Green colour.
(If we assume that the box that contains Green colour is at the 5th position from the top then the box that contains Orange colour would be at the 4th position from the bottom and in that case we would not be able to place the box that contains Pink colour. Thus, the box containing Green colour is at the top and the box containing Orange colour is at the second position from the top and accordingly, we can place the boxes containing Pink and Red colour.)

4) The box that contains Yellow colour is kept immediately below the box that contains Blue colour.
There are two possibilities here:
Case I: The Blue box is kept immediately below the Orange box and the Yellow box is kept at the 4th position from the top.
Case II: The blue box is kept at the 2nd place from the bottom and the Yellow box is kept at the bottom.
5) Only one box is kept between the boxes that contain Brown and Yellow colour.
(Let us assume that the case II of the previous statement is true, then the Yellow box is at the bottom but in that case we would not be able to place the Brown box so that it satisfy the given criteria. Thus, the blue box is placed at the 3rd position and the Yellow box is placed at the 4th position from the top. Also, we cannot place the Brown box above the yellow box in this case as the orange box is there. Thus, the Brown box is placed two boxes below the Yellow box.)

6) The box that contains Black colour is not kept at the bottom.
(Implies, the purple box must be at the bottom and the black box must be right above the purple box as it is the only possibility left.)

Clearly, the box that contains the Blue colour is placed immediately below the box that contains Orange colour.