Welcome to 2CarPros.
I copied your picture and circled where there should be plastic clips integral to the mount. The base should push back into the headliner. Now, the headliner itself may have worn and the clips will no longer hold the base, so confirm that isn't the issue.
Simply place one side of the base in the headliner and swing the opposite end up until it is flush and holding. The light fixture then simply clips in from that point. The white clips at the bottom is what holds it in place.
Let me know if this helps or if I made things worse. LOL
Take care,
Joe
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Friday, September 20th, 2019 AT 7:35 PM