Amount of application storage is wrong and blocking hard drive space

Let's see if we can f=ind where it really is...

Have you emptied the trash lately?

Terminal code to clean DocumentRevisionsfolder…

https://apple.stackexchange.com/questions/313102/what-will-occur-if-the-documentrevisions-v100-folder-is-deleted

macos - What will occur if the .DocumentRevisions-V100 folder is deleted? - Ask Different (stackexchange.com)

System Memory OS 10.12.6 Sierra - Apple Community

Look for iOS backups…

/Users/YourUserName/Library/Application Support/MobileSync/Backup

OmniDiskSweeper shows you the files on your drive, largest to smallest, and lets you quickly Trash or open them.

https://www.omnigroup.com/more/

Purging local backups

Please note that although this doesn't affect your remote backup from Time Machine, this will get rid of the redundancy (at least until the next Time Machine backup) that a local backup disk will provide. If you need such redundancy or are worried about the recovery of your data then you would be best served to let macOS determine when to purge these files.

Start Terminal from spotlight.

At the terminal type tmutil listlocalsnapshotdates. 

Hit enter.

Here, you'll now see a list of all of the locally stored Time Machine backup snapshots stored on your disk.

Next you can remove the snapshots based on their date. I prefer to delete them one at at time. Once my "System" disk usage is at an acceptable level, I stop deleting but you can delete all of them if you want to reclaim all of the disk space.

Back at the terminal, type tmutil deletelocalsnapshots YYYY-MM-DD-HHMMSS , where will be one of the dates from your backup. This will be in the form of xxx-yy-zz-abcdef. Try to start with the oldest snapshot.

Hit enter.

Repeat for as many snapshot dates as required

http://www.thagomizer.com/blog/2018/03/27/cleaning-up-time-machine-local-snapshots.html

tmutil deletelocalsnapshots /  # deletes all the snapshots

Thanks to BobHarris file sizes, Applications -> Utilities -> Terminal:...

sudo du -hx | sort -h 

sudo du -hx ~/| sort -h 

Transfer files between two Mac computers using target disk mode - Apple Support (CA)

And if your are lucky - you can move enough personal files Off this computer and allow you to ------ >>>

Rebuild the Spotlight index on your Mac

What is “Other” storage on a Mac, and how can I clean it out?

Free up storage space on your Mac

OmniDiskSweeper Safe to use

GrandPerspective 

How to delete Time Machine snapshots on your Mac

See used and available storage space on your Mac

Locate backups of your iPhone, iPad, and iPod touch

Notation - If the user is using a cloning software like Carbon Copy Cloner - suggest tweaking the Safety Net Feature in this software. It may be making addition Snap Shots that are not being Cloned to the Eternal Drive. If this should be the case, these Snap Shot could be using additional space on the drive 

The final word from Apple on Managing the " Other/ System Data “ Category

Other / System Data: Contains files that don’t fall into the categories listed here. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins. You can't manage the contents of this category. The contents are managed by macOS, and the category varies in size depending on the current state of your Mac.

Apple hid the Users' Library folders...

Method 1:

1. From the Finder, select the Go menu at top of the screen, and choose Go to Folder.
2. In the window that opens, enter ~/Library, and click Go.

~ tilde indicates  your home folder