You have to be root to write to /home
So you should run "su" to be able to create the directory.

btw, if you type 'ls -la' you can see the access rights of each file and directory.

drwxr-xr-x 2 root root NAME
for example means (explained from left to right)

it's a directory (the d in the above line)
the owner has read, write and executable rights (rwx)
the group has read and executable rights (r-x)
the others have read and executable rights (r-x)
the owner is root
the group is root

You can use 'chmod' to change these settings.
E.g. chmod g+w NAME to allow the group to write
chown and chgrp may be used for changing the file's owner and group