Unable to mount exFAT external HDD on Mac

another reason MacOS will not mount a Volume is that its Directory is damaged.

launch Disk Utility, and use the tiny View menu to choose "Show all devices"

select in turn and click on RepairDisk/FirstAid for each of:

The Physical device, and

The ExFAT Volume

if any errors are found run again until to comes clean

post back with your results

Pcfreak wrote:

I have a problem I can't mount the external HDD

https://discussions.apple.com/content/attachment/4e11f619-c887-48ec-bc8b-59230df169ce

for what purchase?

old or new?

DiskUtility>View>Show all devices you are erasing /reformatting/initializing the Parent drive (top most) not a child volume.

Erase and reformat a storage device in Disk Utility on Mac

Erase and reformat a storage device in Disk Utility on Mac - Apple Support

Apple only(?) then use GUID/ APFS

macOS has native support for exFAT — no additional drivers required.  

• Restart your Mac: A simple reboot can often resolve unexpected issues.  
• Test a different USB port or cable: Faulty connections are a common culprit.  
• Try another Mac or Windows PC: If the drive works elsewhere, the problem likely lies with your macOS setup.

Now you have the answer. The Mac does not consider that Volume Directory free of errors, and will not use it in its current form.

Have the PC read the files and use Mac File Sharing to send the files from one computer to the other.

Or try using PC tools to Repair the Directory.