how to crop without losing resolution

Imagine that your original is 3000x2000 pixels. When you are printing at 300 pixels per inch, that becomes a 10"x6 2/3" print. If you print that same image on a 6x4, you can either keep the file as is and your print is now 500 ppi. However, most printers such as the photo printers cannot print at such a resolution, so what you can do is scale down the original image to be 300 ppi at 6x4. This is 1800x1200 pixels. So the original pixels in the original image have to be averaged and interpolated to show the same image but in fewer pixels. This is downscaling. You can do this scaling yourself in the Lightroom export panel, or you can let your printing service take care of it for you.