Hook: Wall Medium (Blue Square)The Art: Red Bisector decoration fits into a blue medium square wall hook.
Hook: Wall Large (Purple Rectangle)The Art: Red Bisector decoration fits into a large purple rectangle wall hook.
How to Get an Art: Red Bisector Decoration
Reputation decorations are a type of decoration that can only be earned through reputation. Players who have the correct reputation rank can buy reputation decorations from a reputation vendor, usually with a special currency, and list them on the GTN - but players that buy them from the GTN MUST still have the correct reputation rank to actually use them. For the Art: Red Bisector decoration you must have reputation with Hero with the Gree.
To gain reputation, you must do special quests or certain heroics for various factions across the galaxy. To see your reputation, open your legacy menu. Some reputation decorations require special tokens to purchase form the reputation vendor, and other require crafted Universal Prefabs. It's always worth checking the GTN to see what people are selling them for - you might save yourself some tokens or the cost of a prefab.