Well, think about it. A 4x6 print isn't the same shape/ratio as a 5x7 print. Neither is it the same shape as an 8x10 print.
So if you order one of those other sizes, the shape (aspect ratio) will not match the 4x6 shape (2:3) ratio. So the result is that your photo has to be cropped. (the alternative would be to squish your image to fit the new size, but nobody wants that
So before you order one of those other sizes, crop the image yourself to the proper shape/aspect ratio. That way, you can decide what gets cut off and what doesn't.
If you don't like your options for how to crop, then choose a size that does match your pictures size. So rather than an 8x10, you could print an 8x12...and so on.
Also, experienced photographers will often shoot 'loose', giving themselves room in the photo, so that they can easily crop when needed.