How can I open a specific port on OS X 10.11.13
You can use the terminal command nc -l 4444 to create a server that listens on port 4444.  However, I think your question really is about opening a port on your router.  If someone else out on the internet somewhere is trying to connect to you on port 4444, the router you have acts as a boundary between you and them, and most often all incoming ports by default are closed.  So even if you run a server on your Mac and it's listening on port 4444, traffic on that port needs to be allowed through at the router level.

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