I don't have the up anymore, but we used a L bracket- DH drilled one side in to the box, then cut a notch on the other side. He put a screw in the wall and slid the notch over the wall screw. There's probably other ways of doing it, but it worked for us!
We fastened the L brackets to the cornice box and then mounted on the wall. If you have drywall be sure to use anchors or make sure it's mounted into the studs!
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Re: Come in if you have a cornice box...
This link has hanging instructions if you scroll all the way down to the end of their DIY tutorial on making cornices:
https://www.prudentbaby.com/2009/11/diy-cornice-pelmet-how-to.html