Sharing can be a little bit odd at first in the Backpack (and it is something we know needs work) but essentially you don't share individual badges, you share out your collections.

To create a collection log into your Backpack account and hit collections at the top. You can then drag badges over into their own mini collections (you can make as many as you want). You'll then be able to see the share icon in the bottom right corner of the collection which will allow you to push to Twitter, Facebook, Google+ and LinkedIn. You also need to ensure your collection is set to 'Public' using the checkbox provided.

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