The Goat Shelter requires eight Goat Bedding, eight Hinges, and eight Nails to complete. All of these items are earned through a combination of general news posts on your wall and individual requests sent directly to your neighbors. Once that's done, you'll need to ask four of your neighbors to come work as builders within the Goat Shelter to actually finish it off.
With the building out of the way, the Goat Shelter can hold up to 12 Prized Goats, regardless of type (e.g. you could store a Prized Red Goat alongside a Prized Pygmy Goat). Each individual animal will take up one storage slot. You can feed all of these Prized Goats at the same time for half of the Animal Feed it would take if they were still wandering around your farm.
In addition, once you finish building the Goat Shelter, your maximum Animal Feed capacity will go up by 35 points. It's also worth noting that you'll still receive all of the normal products from your Goats as you tend them. That is, they'll still produce Goat Cheese each time they're fed, whether they're inside the Goat Shelter or not.
Unfortunately, this building has yet to roll around to all farmers, so if you don't see one in your game just yet, you'll need to wait just a bit longer to build one. Hopefully, the wait won't be too long, and you can reclaim some of your land space soon.
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Have you already received your Goat Shelter in FarmVille 2, or are you still waiting for this event to roll around to your game? Do you have enough Prized Goats to make this building worth constructing? Sound off in the comments!