A synthesis paper simply means that you are taking something you have become familiar with and repackaging it in a new and creative way.
If you don't have any text books to work with, I would use the internet to research areas about reading that might peak your interest. Try collecting these through "Google Alerts".
Once you've located your interest, approach this by using a double entry journal method (you can look for this online as well). As you read your selected text, jot down what comes to mind. At the same time annotate the word, phrase, or line in your text that prompted your thought. When you have completed your reading, you will have a wonderful collection of notes from your own thoughts about the subject that has been assigned.
This is a very open assignment and does not "pigeon-hole" you into any one particular mind set. It may seem difficult at first, but once you get going, I think you will enjoy it.