Instructions
Visit the Botanicus room and view the garden. Speak to the bot gardener to receive the first clue to solving the quest's puzzle.
Visit the rest of the garden rooms: Chlorophyllum, Sylva and Nox. Speak with the bot gardener in each of the rooms; through reading the gardeners' hints, you should notice the repeated word is "love." This is the solution to the puzzle.
Return to your room in the hotel and click on the Garden Seed. Enter the solution to the puzzle and watch your seed mature into fully grown plants. You will also receive a Flower Badge and possibly the Wonder Lamp.