If you can get the for images onto a page in the order that you want them then you can change the print destination to file and you can print that to a JPEG file that can be sent to the printer. But in order to make it 16 x 20" it seems to me that you would have to have printer that supported paper that big. I don't know if the exported JPEG would be large enough for what you are looking for or not.
1. Select folder or collection containing the 4 images. Go to Print module.
2. Click Page Setup: select 16x20inch paper (landscape or portrait) My image is A2.
(I don't know what to do here if you don't have a connected printer that is capable of 16x20inch. Although my printer prints up to 8x10inch but shows larger paper sizes in its setup dialog. Maybe other experts have this answer.!)
3. Select "Custom Package" (Allows your desired sort order!)
4. In "Rulers Grids & Guides" tick for ON, Set Grid Snap=Grid
5. In "Cells" Panel: Add to package 8x10inch cell. Repeat for 4 cells.
6. Click on each cell to adjust size, drag position, or rotate.
7. Drag each wanted photo into desired cells from the film-strip- your sort.
8. Set "Print to JPG": Click "Print to File, and save the new 16x20 JPG image for commercial printing.
It took me a while to find "Print to Jpeg" then I stored the image on an external HD and couldn't retrieve it. So the only choice was to store it on the computer HD, Then I could send it. Thanks Richard Haars