Please note that BOTH answers are correct. There are seven "canonical" colors. R O Y G B I V . Many people, however, do not perceive indigo as a separate color from blue or violet, so that makes it six... Six or Seven are both "normally acceptable answers."
But as many of the OTHER posters have said, the edges of those canonical colors fade together. You get reddish-orange and orangish red and so forth. there's no sharp line where you can say "THIS IS RED and THAT IS ORANGE" although there are clear "bands of color" So, in another sense the answer is "an infinite number, since ever different wavelength of light is a color, and all the colors in the sun are there."
BUT BUT BUT BUT
The answer is _not_ "all the colors there are" because color perception is a function not only of wavelength but of saturation.
So, something that is of color blue, but very very dim, looks different than something the same color of blue, but very very bright. Also, some of our color perception comes from MIXING colors, and the rainbow UNMIXES them.
To put that another way, there is no "Purple with a greenish cast" in the rainbow. Neither is there "blue with a hint of yellow." The colors are all separated out.
So, the answer is 'Usually seven, but six for some people, but you can argue for an infinite number as they fade together."
Good luck