iTunes library is split on two hard drives, help please

I have two hard drives on my computer. An SSD with the OS and an HDD for mass storage. When I first got this computer, I put my iTunes library on the HDD, but for some reason, anything I added to my iTunes library since then would go to the SSD. I guess I had to manually choose the destination to be on my HDD...anyway, eventually I came to realize that lots of music was being stored on my SSD. My SSD is 256 GB in capacity and I have plenty of room, no big deal. I didn't solve this issue in the past as I didn't know how to go about doing it and just said "I don't care, I'll figure this out eventually". So over time, more and more music has been added to the iTunes folder on my SSD.

I want to back up my music library to an external HDD. Now, what can I do to solve this problem? I googled how to back up an iTunes library to an external HDD (for PC) on google and the apple website says something about consolidating your itunes library before backing it up to an external HDD. It said something about putting your library all in one place, and if you'd like, you could delete the data if it is someplace you don't want it to remain at.

So I'm not completely sure on this, but this seems like this would solve my problem, would it not? I just choose the HDD as the destination when consolidating my library. Is this consolidation process the solution to my problem?

iTunes library is split on two hard drives, help please