So, in this particular case, I think you have some options not necessarily always available. That's because your photo is really almost the required resolution — just the wrong shape.
It looks like the rule behind the recommended sizes you've given is simply 150 pixels per inch. That is, 20" × 150 pixels = 3000 pixels per inch, and in the other dimension, 16" × 150 pixels = 2400 pixels per inch.
Your image is sufficient in the long dimension (3008 — we'll ignore the slightly odd extra 8, which is typical for camera output; it's such a tiny bit that it's really negligible), but doesn't measure up in the other dimension. That's because it uses the
3:2 aspect ration typical for DSLRs. The canvas sizes, however, are in a
5:4 ratio — a classic photographic shape, matching the venerable 8×10".
So, in order to make your image fit, you need to do one of two things. First, you can lop off the ends of your image, taking a 5:4-ratio square from the middle. In order to make that work, you'd take 254 pixels off each edge, leaving you with 2500×2000. But now, clearly, you're under the limit. Now, personally, I think that you probably can get away with upscaling by 20% to make the web site happy. With a canvas print, this'll probably look just fine unless someone has their nose all up in it.
Alternately, you can "letterbox" — just as with a wide-screen aspect ratio movie on an older 4:3 TV, you put 200-pixel black (or white, or whatever color you want, really) bars on the top and bottom, so the whole image overall is 3000×2400. Problem solved — except that might look funny.
So, the final possibility (and I think the best option, unless your image is really amenable to the 5:4 crop) is to find a print service that will do canvas prints in dimensions that fit the 3:2 aspect ratio. Bay Photo is one such well-regarded print service, but there's others as well. Then, you could get something like a 18"×12" canvas. (Bay Photo actually requests 300dpi sources, but they'll let you use lower ones if you promise not to complain about the results.)