Yes, you can do that by clicking on the request, but it will probably delay your getting the book! 

This is because:

• If the requestor cancels, the book will go back onto the sender's bookshelf
• If the order is then re-submitted, it will go to that same sender.
• If you still want the book, it is best to let the system handle the request automatically!
  • If the sender doesn't respond within 5 days, your request will automatically be passed along to a new sender
  • You can tell that this has happened because the Requested on: date will change on the request
  • You will not get an email telling you that this has happened.  This is not done to drive you crazy; we want to limit the number of PBS emails cluttering up your inbox.
• It may be hard to wait, but just know that PBS will get the book for you as quickly as possible, and you don't have to do a thing more after requesting it!
• If the sender does not respond, and there is not another copy of the book available in the system
  • The request will be canceled, you will get your credit back, and the book will go onto your Wish List
  • You will get an email from PBS if this happens.

Related Links:

What happens after you submit a request for a book
What if the sender does not respond to my request within 4 days?
What if the sender agrees to send the book, but doesn't mark it mailed before the deadline?
What if I want to cancel a request I made?
How can I tell who's sending me a book? (or to whom I am sending a book?)
When will I get my book?
What are the differences between the Reminder List and the Wish List?
Box-O-Books Tutorial Step 4: Boxer Negotiation
What is the Wish List?
How the Wish List Works