I'm looking for a program that will allow me to print 4 different 4×6 photos on one 8×10 sheet of photo paper with my HP Envy 5540.
HP has created an application HP Photo Creations. It has been developed exactly for the process you've explained above. Access the link posted below to install it. It's available for both Windows and Mac. Visit the link below to download the application for your operating system.
Once installed, add some images and then you can print them.