it is often recommended to have ~ 50GB of free space to apply an upgrade. the ~12 GB file size of the upgrade is very deceiving. there also needs to be room enough to expand the file as well as free space to "shuffle things around" while the upgrade is being installed. and it's also a good practice to keep ~ 20% of the local drive as free space for optimal operation of your Mac.
if you are running low on space, you can purchase an external HDD or SSD of sufficient capacity and move your larger files (videos, pictures, documents, etc...) to it. once they are on the EHD, you can simply erase the same files from your internal drive. and, if it's just going to be used for storage, you can use an HDD and save a few bucks over the cost of an SSD. FWIW, i personally keep very little on my internal drive.
also, you may want to read these two articles:
Optimize storage space on your Mac
How to free up storage space on your Mac