I’ll have to defer to the Mac experts here since I’m a Windows guy. It appears, though, that they want you to bring up a ‘command prompt’ which will allow you to type in the ‘bash’ command. Sorry, I don’t know how you’d do that on a Mac.
I doubt the problem is there... the DNS resolver cache clears every 24 hours automatically. If you are still having the problem after not using the computer for 24 hours, it's probably not the cache.
By the way, you should leave your Mac turned on... it does housekeeping tasks after there has been no user interaction for three hours.
However, the "terminal" is an application in your Utilities folder called "Terminal" (for some strange reason) that gives a user access to the entire command set of UNIX. It's sort of like DOS. Run the Terminal and type the command in the window and press RETURN and see if it fixes your problem. It can't hurt.