Pandas are one of the three starter pets. Panda quest givers tend to offer easy quests.
Go straight through the rock archway and follow the path. You can take either pathway, they both lead to beige/cool yellow steps in between them. If you take the purple path take an immediate left after and you should see the steps. If you take the other path, it's a right and you should see them as well. The building of interest is nestled in a white bamboo garden. Go up the steps and towards a red cage which contains the Panda egg. Enter the house and speak to the giant panda. Do as he says, which is plant 20 bamboo seeds in his garden right outside and next to the red panda. Seeds can be found around his house. Once that is complete, speak to him again and obtain your prize.