There is no Apple-provided key combination that changes the color of your
Macintosh desktop. If you've seen someone change the desktop color this
way, it was most likely with a product that was used to automate the
process of using a control panel to change the desktop color. Look for
third party macro programs like QuicKeys which may be able to accomplish
this for you.
For more information, search on "CE Software" and "3rd".