Like many others, I have thoroughly searched all the possibilities of work over the Internet, including those via Facebook. I've found two ways that Facebook can bring you a profit:
1. Create a Facebook sales page. I am sure that your Facebook profile is full of requests for you to like the pages where something is sold or offers some service. Some of them have a large number of followers and they do quite well. And everything is being sold - from needle to locomotive.
On Facebook pages, you can literally open your online shop to have your little job from home.