To troubleshoot HP fax error code 346, start by ensuring the phone line is free of interference and properly connected. Verify that the recipient's fax number is correct and functioning. Try resending the fax after removing any possible line noise or interference. If the issue persists, contact the recipient to confirm their fax machine's compatibility and settings. Additionally, check for any recent changes in fax settings or updates on your fax machine. Reset the fax machine and try sending the fax again. If the problem persists, contact your telephone service provider to inspect the phone line for any issues affecting fax transmission.