Rethread your machine making sure the top thread is through the tension disk. Hold the thread off the bobbin in one hand and the end of the thread (after you've threadded it) and tug on both ends. That should make sure it's in the tension disk. Next make sure your bobbin is seated properly in the bobbin case. There's a tension like thing there too. Put your finger on the bobbin and pull a little on the end of the thread after you threadded the bobbin. If your tension area has a dial with numbers on it, put it in the middle. Looking at your sample, I think either the top thread or the bobbin is not in a tension disk. What kind of machine do you have?
You have one quilt started and want to put that side to do another - that's a sign of a true quilter! :D
Also, you should come into the chat room next time you're online. Click on the "live chat" button at the top of the site. Anyone there will be happy to help you out.