I am new to Linux and command line. How do I move a directory under Linux operating systems?

To move SOURCE directory to a DEST directory use the mv command as follows:

mv source dest
mv /path/to/source /path/to/dest

In this example, move /home/vivek/data/ directory to /nas/home/vivek/archived/ directory:
$ mv /home/vivek/data/ /nas/home/vivek/archived/
OR
$ cd /home/vivek
$ mv data/ /nas/home/vivek/archived/
To get verbose output (explain what is being done), type:
$ mv -v /home/vivek/data/ /nas/home/vivek/archived/

How do I Move Multiple Directories?

Use the following syntax to move dir1 and dir2 to /path/to/dest/ directory:
$ mv -v dir1 dir2 /path/to/dest/
$ ls -l /path/to/dest/
OR use the following syntax:
$ mv -v /home/vivek/dir1/ /home/vivek/dir2/ -t /nas/home/vivek/archived/