How do you print a 4 x6 photo keeping full frame from a cell phone image?

When printing an image that has one aspect ratio on paper that has a different aspect ratio, there are two options if you don't want the image "stretched" in one direction. You either crop the image to match the aspect ratio of the paper, or you print the image "letterboxed" - I.E. With borders on one or two sides that you can trim off, making the paper match the aspect ratio of the image.

Technically, I guess, there's a third option between the two - crop a little bit less so the borders are a little smaller - but that's a compromise you need to decide on.

Most printers will default to cropping the image, but should have the ability to print the whole image if you ask them, although that may be less true with the cheaper fully-automated places.