In practice f-stops have discrete values; in other words, lenses have a finite number of f-stops available, with no intermediate options. The standard f-stops are as follows:
1.0 | 1.4 | 2.0| 2.8 | 4 | 5.6 | 8 | 11 | 16 | 22
Armed with this knowledge, using the Nikon Teleconverter TC-20E II with the Nikon AF-S 300mm F/4 lens would simply allow you to shoot at 600mm (900mm at 35mm format) F/8 (two stops down from F/4). Not brilliant but otherwise, still useable.