Hook: Floor Small (Green Square)The Ancient Archaeological Find decoration fits into a small green square floor hook.
Hook: Floor Medium Narrow (Blue Rectangle)The Ancient Archaeological Find decoration fits into a narrow blue medium rectangle floor hook.
Hook: Floor Medium (Blue Square)The Ancient Archaeological Find decoration fits into a blue medium square floor hook.
How to Get an Ancient Archaeological Find Decoration
Every time you complete your personal conquest, you receive a lockbox with three random conquest Crafting Node Decorations, one of which could possibly be an Ancient Archaeological Find. You get a second lockbox if you complete your guild conquest goal as well.
If you're looking to get an Ancient Archaeological Find and haven't gotten lucky with your conquest rewards, you can buy one from the GTN from another player. These decorations are farily inexpensive because there is an unlimited supply - more are created every time someone finishes their conquest goal.