You almost got this, you are just missing step i), you want to put the animal object into the num_pets array, as opposed to just the animal name:
i) Find the animal that the user selected in the animal hash; 
ii) Remove the animal from the animals hash; 
ii) Add the animal to the clients num_pets array; 

    animal = shelter.animals[adopted]
    shelter.animals.delete(adopted)
    shelter.clients[adopter].num_pets << animal