DDR3 is reasonably tolerant of mixed ram.
Likst the make/model of your motherboard as well as the ram specs that is now installed.
CPU-Z will tell you the motherboard and the memory and spd tabs will identify what you have.
If possible, install the two 4gb sticks on one channel and the new 8gb stick on the other channel.
That way you will run in faster dual channel mode.
If all looks good,
Run memtest86 or memtest86+
They boot from a usb stick and do not use windows.
You can download them here:
MemTest86 is the original self booting memory testing software for x86 and ARM computers. Supporting both BIOS and UEFI, with options to boot from USB.
www.memtest86.com
Memtest86+ is an advanced, free, open-source, stand-alone memory tester for 32- and 64-bit computers (UEFI & BIOS supported)
www.memtest.org
If you can run a full pass with NO errors, your ram should be ok.
Running several more passes will sometimes uncover an issue, but it takes more time.
Probably not worth it unless you really suspect a ram issue.