Does both monitors when connected at the same time show up in Windows Settings - Display?
In Device Manager are there any errors under "Sound, Video, Game Controller" or any error Device Manager errors in general?
How do you have your second monitor connected to the GPU card? Are you using an Adapter convertor cable?
Do you have your Monitor's driver installed in Device Manager?
As an example only here is my Device Manager:
I have all three of my monitors drivers installed but I only use one Monitor at a time but sometimes I use 2 monitors at a time but all are connected to my GPU card.
In my Window's Setting I have both my 4K LG PC Monitor and Samsung 2k TV showing a Duplicates with my LG Monitor check marked as my Main Display Monitor:
Monitor number 3 is actually my AVR which I have connected via HDMI from my GPU card. It has no sound.
But I have no sounds coming from either of them because when I use my Bluetooth Headphones that becomes my Default Audio Device but when I disconnect the headphones my LG Monitor automatically becomes my Default Audio Device with sound.
My Windows Sound Panel as an example only: