What you're attempting to do would seem to be mathematically impossible (unless you make your grandchildren look fatter or thinner, in the same way that fairground mirrors do!).
If you want exactly the same photograph, but bigger, making the shorter edge 8", instead of 4", would mean doubling the longer edge up to 12".
Alternatively, changing the longer edge from 6" to 10" would force the shorter edge to be 6.67" (to 2 d.p).
So (without cropping something - or stretching your grandchildren!) you can have an 8" x 12" photo, or a 6.67" x 10" one, but you can't have an 8" x 10" one.
If you're determined to end up with an 8" x 10" result, you'll have to decide where cropping can occur. (i.e. top/bottom or left/right).
It's probably simplest to 'play' with the photo until you get it right. You don't need any specialist photo-manipulation software; you can just use Word. Open a new document, using either 'portrait' or 'landscape' format, to match the photo. Go to Insert > Picture, navigate to the location of photo and double-click on it. Click and drag the 'handles' at the corners of the photo (not at the edges) until one edge is the required length (either 8" or 10") and the other one is 'a bit too big'. Then print the photo (using the 'high-resolution' settings available with your printer, and using photo paper ) and trim off the excess with scissors. (If in doubt, do a test print on normal paper first).
Chris