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@Peanut7139 , this is what you do:
In the picture above the Pet is thinking of a burger, so drop them on the burger bar.
In Winter Petopia they also ask to go skating on the lake.
Drink juice at the bar, as seen here from a previous Petopia:
Play at the Arcade:
and go to the open stage
Each time you get a new special building it brings activities for the Pets.
Those mentioned above are all that I have so far this time. Let me know if you have another that I've not mentioned.