Whatever it is that you are trying to add to your iPod is larger than can be fitted onto it. Check the size of the selection that you are trying to add to the iPod.
The actual storage capacity of an iPod is less than the capacity mentioned (due to the operating system etc.), so If your iPod is a 4GB device, then I'm guessing that the actual storage capacity will be about 3.5GB (but note that that is approximate). Since the error message states that an additional 6.03GB is required, that means that the selection that iTunes is trying to add to the iPod is approximately 9.53GB in size.
Try deselecting the playlist you mentioned and then tap the Sync button. In theory, iTunes will go through the steps to sync but since there is nothing to sync, the iPod will remain empty. However - if there is something else selected, that you had not noticed, I would expect one of two things to happen:
- songs appear on the iPod that you had not realised had been selected
- nothing is added to the iPod, but a message telling you that additional space is required appears again. This time however, the space is smaller than before. Again, this tells you that there is still something selected to sync that you did not know about
I assume that you are using sync selected playlist, artists, albums and genres, in which case perhaps there is something selected in the selection area (that is out of the display area) that you are not aware of. See the screenshot below: