Is a 1936X1296 a printable 4X6 image?

On my Nikon D200 camera I have choices of image sizes small is 1936X1296/2.5M, a medium is 2896X1944/5.6M, and a large is 3872X2592/10.0M. What size the right size to put in the camera to print 4X6 pictures?

The small size will print fine at 4 x 6, however, it is never a good idea to set your camera to anything other than it's largest size / highest quality option. If the time comes when you take a really great shot and you want a photo larger than 4 x 6, you are not going to be able to make a quality large print with your camera at the smaller size. You can always downsize a photo with no problem, but you can't make it larger without hurting quality.

Also, why pay for a good camera and then cripple it with a small size option? You are basically using a fine camera as a cheap 2 megapixel point and shoot when you set such a small size and reduction in resolution. You paid for a quality sensor that is designed to output at it's maximum size and quality. Why not use it as such? The only thing that can make sense for the lower setting is if you are shooting some type of event and are printing 4 x 6 photos on the spot. Otherwise, keep your camera at it's largest size / highest quality setting.

It's a tad over kill, but yes, very well.
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A 4x6 really only needs 800x1200 pixels (or any number of pixels falling into that ratio, and larger). If you have a RIP or other printing software where you can just tell it what size you want, it don't care what the so called DPI is and only works on available pixels, and gives you what you ask for. If not enough pixels, the program may say so and suggest you to not print it.
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I too have a D-200, however, it has been re-vamped by Fuji into their S-5 Pro using Fuji's Super Hex CCD chip and related electronics. IMHO, being a dealer of digital equipment for a number of years and could test side by side different makes and models, found it to deliver a better image. My Small, Medium and Large is - 2304x1536, 3024x2016 and 4256x2848 which roughly equal 3, 6 and 12Mp.
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RIP = Raster Image Processing. Do you know or understand what a Raster Image is?
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With the right printer interface program you can command it to print 4x6 from what ever is in the folder you aim it at. It will print 4x6. Period. It's not rocket science if you get the pesky DPI concept OUT of your train of thought and remember, it is All pixels. There are NO DPI's in a digital image. It is PIXELS, and they don't cross correlate, in reality. You can 'make it 'relate' in words, somewhat, but then it starts getting muddy again.
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It takes at least 180 to 200 PIXELS per inch, of photo you want to make, with out a RIP program… It's easire to remember 200 and to do the math in your head.
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A 8x10 = 1600x2000 PIXELS, but you need a program where you can TELL it to pring a 8x10 from this.
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Knowing this ratio, you can crop and cut up a larger image to EXACTLY what you want when printing.
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I shoot virtually at 6Mp most of the time, in RAW + Jpg or sometimes just Jpg depending on the reason. However, even in 6Mp mode I have made 16x20's and 20x24 inch prints on my Epson 7600 wide format printer using Q-image RIP printer software. I won't go into the "magic" and real science here but ask a pro print lab if they use RIP in their printing. On some occations I have gone 24x36 that look like ISO 400 or 800 film!
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Your camera will do full size photo quality prints, and smaller, on a 13x19 printer, easy, if you understand printing. But with a RIP driver and a larger printer.larger quality prints OR - print packages like graduations and weddings where different sizes are inter mixed on 1 sheet can be offered.
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Read the Myth of DPI - http://www.rideau-info.com/photos/index.html.