To sell the animals in your Giftbox or Item Storage, go to the Market. When you see Toms Message that pops up, click on I want to sell.... then click on OK show me your prices.
Your Storage will open. There are 3 sections at the top called Storage, Gifts and Items. Selling Gifts in your Giftbox: Click on the Gifts section to sell animals in your Gift Box and you will see what is currently in your gift box and can click on Sell All on the animals that you want to sell. Selling Animals in your Item Storage: Click on the Items section to sell animals in your Item storage. Change the A-Z filter top right to Animals to see just your animals in Item storage. Then when you see the animals that you want to sell, you can click on Sell All or Sell Half to sell them or about half of the quantity, if you do not wish to sell all of them.
Selling Animals in your Giftbox or Item Storage