I was about to respond, and noticed the first answer. It is good as far as it goes, but I have a couple more points that might be useful...
A. 'She read the book to the desk.' -- Unusual, but if there is a group of people sitting at a desk -- perhaps a jury of some sort, or a group of judges -- they can be referred to as "the desk", and if she read the book to them, them this is a context in which the sentence is possible. You might read to the desk itself, but this would be a rather strange activity -- unless the desk contained a video link, and by reading to the desk, she is actually reading to the video camera!
B. 'She read the book at the desk.' -- 'She read the book (while sitting or standing) at the desk.'
C. 'She read the book from the desk.' -- She was sitting or standing at the desk and read the book from there. This formation is fairly common in referring to speechmaking, or church readings: 'She read the speech from the podium.' 'She read the lesson from the lectern.'
D. 'She read the book on the desk.' -- 'She read the book (that was lying) on the desk.' 'She read the book (as it lay) on the deak.' 'She read the book (than was originally lying) on the desk.'
ALL the prepositions are valid, if you can find a valid context. So the original question is not as clear as the person setting it assumed!
But if the question was something like "Which preposition is most likely in a well-formed sentence?", then D would probably be the preferred answer.