Daniel from Bolney CEP School wrote saying the following and included a picture:
I found out that you had to start with all four colours on one face. Then I made sure I worked diagonally with the other colours. This meant that all faces could show all four colours.
Julian from the British School Manila in the Philippines sent in the following solution:
(imagine you could see through the top)
Thank you and well done! If you thought it was impossible, have a think about those solutions above.