Such a move requires a computer, even a small one.
I also want to note you should not "transfer" but copy. This way your files are copies in case the Ultra Book develops a fault. Many folk have one last copy and transfer (move) the files then discover the move failed. If they had copied, they would have a second chance.
How would I go about transferring the files on my 2 GB Fantom drive to my 4 GB Ultra Book without actually going through the computer? Is it possible to wire them to each other and then transfer information directly? If so, how would I go about it please? Thank you kindly for your help!