To be safe back it up using cp /etc/dhcp/dhcpd.config /$HOME/dhcpd.config.backup
and run gksu gedit /etc/dhcp/dhcpd.config
Replace gedit with the editor of your choice
you will get such a prompt

Enter your password here
A new window opens and you can edit your config there
In case something goes wrong you can restore it from your backup in the home folder
It is denied permission because of the general system of how linux handles permission
Anything in the $HOME folder belongs to the user, whereas anything under / belongs to root. Any file created in an user accessible folder belongs to that user
the /etc/dhcp/dhcpd.conf file you are trying to access belongs to root, and most files created in a /etc/ belongs to root by default for security reasons
You can still edit this file by elevating your permissions
To do this you have a number of ways
use su which stands for switch user. Without any attributes to it, it functions as a command to switch to the root account
using sudo which elevates your permission for only one command. Its often used only for command-line apps such as CLI text editors like vim,nano etc
using gksu which elevates your permission for only one command, but unlike sudo its used for a graphical program such as GUI text editors such as gedit . it uses a graphical prompt to facilitate entering of a password