If you are refering to paper used in a darkroom then you'll find that 4" x 6" paper is not a precut size. It's actually a large roll of paper that's cut as it's used and dispensed with a roll cassette and roll easel/cutter.
If however you mean photo quality inkjet or similar paper then you should have specified 'injket paper'
Actually in the photo finishing industry a 'photo printer' is an automated printer that uses conventonal photographic papers and chemistry such as an RA-4 printer. The term is also applied to some dye sublimation printers such as the Fuji Pictography series.
The correct term for what you refer to is an 'injket photo-realistic printer' or inkjet photo printer for short.
i usually find that perforated 4"x6" inch papers are expensive. you may get it cheaper by using A4 size photos and print 4 x nearly 4Rs which is much cheaper.....
A4 is 8.27"w x 11.69"h, thus i say you can get near 4R size.....11.69" is still a little short of 2 x 6".....