Which of the following statements in regard to directories is false?

In MS-DOS and modern operating systems, directories (or folders) are organizational structures used to store files. Here's an analysis of each statement:

Directories can exist inside directories:
This statement is true. Directories can contain other directories, forming a hierarchical structure where directories can be nested within each other.

The root directory is always at the highest level:
This statement is generally true. The root directory is the top-most directory in a file system hierarchy. It contains all other directories and files on the disk.

Directories with files can be deleted:
This statement is true. Directories that contain files can be deleted from the file system. Deleting a directory typically removes all files and subdirectories contained within it.

Directories cannot be renamed:
This statement is false. Directories can be renamed in MS-DOS and other operating systems. Renaming a directory changes its name while keeping its contents intact.

Therefore, the correct answer is Option D: Directories cannot be renamed.