It would depend on the scope of the permission, such as “this entry only,” “this entry and sub folders,” etc.

So in your case, you would want the "Read" permission on the parent folder to have a scope of "This folder, subfolders and documents"

Which would provide read access to that folder and anything beneath it.

Guess this is where I'm getting confused.  I don't want them to read other folders only their folder specifically. 

What's the difference between read and browse?

Repository
      Other Folder 1
      Incoming Docs
          Other Folder 1
          Other Folder 2
          Registration
                Other Folder1
                Failures
                    101-Building Name
                          Documents inside
                     102-Building Name
                          Documents inside

For instance I don't want them to see the "other Folders" I thought setting read access on that folder would work, but I set read access from Repository with the scope of this entry only then the Incoming Docs with entry only then.... to the 101-Building Name folder with Read-Browse and other properties.  They can't see the folders though when I do that. I had to add Browse to all the parent folders which allowed them to see the "other Folders"

It sounds like the part that's tripping you up a bit is that you cannot have a gap between folders and still view the children.

Try to think of it like line-of-sight. If you don't have direct line-of-sight to a folder, you won't see it in the repository regardless of your access rights.

Therefore, if any parent folder is hidden from the user it disrupts the line-of-sight for anything below it in the folder tree.

For example,

• REPOSITORY
  • Folder 1 - This entry only
    • Folder 2 - No Rights
      • Folder 3 - This entry only

Although the user has rights to Folder 3, if he/she logs into the repository at the root level, Folder 3 will not be visible because the line-of-sight is broken at Folder 2.

Folder 3 is not a direct child of Folder 1, so it will not appear in Folder 1 since access rights do not affect how the folder structure is presented.

What you need to do is set the permissions AND establish an alternate "line-of-sight" path so they can get to the folder.

There are a couple of good ways you can do this;

1. Create an LFE link the user can have on their desktop that bypasses Folder 1 and Folder 2 entirely and leads directly to Folder 3.
2. Add shortcuts to Folder 3 in Folder 1 to bridge the gap.

For the shortcut example,

• REPOSITORY
  • Folder 1 - This entry only
    • Folder 2 - No Rights
      • Folder 3 - This entry only
    • Folder 3 Shortcut ^

By adding the shortcut, you can bypass the hidden Folder 2 and still provide a path from Folder 1 > Folder 3 Shortcut > Folder 3

Then, you give users access to their respective folder as well as the associated shortcut; only they will see the shortcuts, and it will allow them to navigate to the folder despite lacking access to the parent folder.

I understand the line of sight issue...I just can't explain well. I had a line of sight to the folder with read permissions but not browse.  Still couldn't see the folder. When I added browse then I could see the folder, but all others as well.

Just to confirm, you gave them Read permissions on every folder in the path?

EDIT: I think I might know the problem. Check the Admin console to see if they have Bypass Browse enabled under "assigned privileges"

Browse is needed, but if they have bypass browse privileges it will not hide the inaccessible folders because it skips that check.

I just checked and they are not set to "Bypass Browse"