$PATH error on a terminal
Okay, so you've got a good understanding of $PATH and how it's used, but you're mistaken in thinking that it's a command. In Bash (and other shells), words prefaced by a dollarsign are variables. You can change the value of $PATH with the export command (as you probably already know).

export PATH=$PATH:/path/to/something/you/need/bin

So in your shell when you just type $PATH you're basically telling your shell to run the command /usr/bin/:/bin/:/usr/local/bin:/etc//etc//etc/ which isn't a valid shell command.

@patrix was right, you should use echo to inspect your $PATH. I suspect that the "zsh: no such file or directory" is just your shell telling you that your command doesn't make sense.