4x6 is a 2:3 aspect ratio and 8x10 is a 4:5 aspect you can not simply re-size the 8x10 to 4x6 that would distort the document. You need to crop the 4:5 aspect ratio 8x10 image to a 2:3 aspect ratio first.
Full image 8x10 4:5 aspect ratio. Inside the red line is a 2:3 aspect ratio. Its about 6.6x10 once you make that crop. you can change the image resolution resolution so the image will print 4"x6" if the 8"x10" had a 300DPI its 2:3 crop set to print 4"x6 will have a 500DPI resolution. All you loose are the cropped off pixels. The other pixels remain the same no image quality is lost.
You can always resize you image to fit on any size paper you have. If the image has a different aspect ratio as your paper there will be margins on two side. For example if you have 4" x 6" paper a 2:3 aspect ratio you can retain all the image pixels and simply re-size your 8" x 10" 4:5 aspect ratio image to print 4" x 5" which will fit on your 4" x 6" with 1/2 margin top and bottom.