Hook: Floor Small (Green Square)The Red Vascular Tendril decoration fits into a small green square floor hook.
Hook: Floor Medium Narrow (Blue Rectangle)The Red Vascular Tendril decoration fits into a narrow blue medium rectangle floor hook.
Hook: Floor Medium (Blue Square)The Red Vascular Tendril decoration fits into a blue medium square floor hook.
How to Get a Red Vascular Tendril 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 a Red Vascular Tendril. You get a second lockbox if you complete your guild conquest goal as well.
If you're looking to get a Red Vascular Tendril 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.