At Warp 6, we should be there in just over 16 hours.
Riker's statement demonstrates a common issue running throughout all iterations of Star Trek
, which is the failure of the writers and editors to grasp the true vastness of space, combined with the overall inadequacies of "warp speed" as initially defined by Gene Roddenberry (who also failed to grasp said vastness).
The definition of "warp speed" is that the speed is the cube of the warp number -- hence, warp 2 is 8x the speed of light, warp 3 is 27x, and so on -- warp 6 is thus 216x the speed of light.
It is a simple calculation from that to see how far 16 hours at warp 6 would take you -- 216/365= .6 light years/day. (.6/24)x16= .4ly in 16 hours. This distance, while it may seem like a lot, is actually only 1/16th the distance from Sol to the nearest star, and is, depending on your definition, barely outside of a solar system, well inside an equivalent Oort Cloud likely to be found around any star.
In the overall case, warp 8, being 512x the speed of light, means it would take you a year to go 512 light years -- which seems like a lot, but, with the galactic diameter being 100k ly, is only 1/200th the size of the galaxy. Add to that the "cubic" element of space and you begin to see that the Federation's maximum volume is but a tiny portion of the entire galaxy, as is Ferengi and Romulan space, since their speeds are comparable. This also wreaks havoc with the ability of a ship, such as the Enterprise
, to go anywhere and have "regular adventures" even a few weeks apart -- a week or two will get you to the next solar system, sure, but hardly far enough that you wouldn't be constantly bumping into people and things you saw last week, yet, for ST:TNG, there is very little week-to-week continuity (This latter is less notable in the later series, but the distance factor is still an issue)..
This problem is most notable in the first season Star Trek: Enterprise
episode "The Andorian Incident,
" which takes place at a known location under a fixed timeline from a given starting point (Earth) and for which previous episodes would be almost impossible to achieve given the stated warp capabilities of the NX-01, and, in addition, suggests that the Klingon home world would have to be only a very short number of light years from Earth.