Hi @shadow_42,
Welcome to HP Forums, this is a great place to get support, find answers and tips.
Thank you for posting your query, I'll be more than glad to help you.
I understand that you get a message "A carrier access code is required" when you try to send a fax from your HP OfficeJet 6962 All-in-One Printer.
This issue could occur if there is a code set by your carrier for long distance fax.
Let's go through a few steps to troubleshoot this issue.
And here's the step by step guide for you in the link: Faxing with Long-Distance Access Codes, Calling Cards, or Internationally
You may also check the link on how to setup fax from the link: How to connect your HP Fax Device to an ISDN, ADSL, PBX, or VoIP line
Let me know how this works.
You have a good day ahead.
Rainbow23 - HP Support.