External hard drive will not mount

I bought a Mini Mac from Apple last month and my 6 TB external hard drive with 30 years of images, mounts on other Apple computers (my 13" Macbook, for example), but not on the Mini.

If I leave the HD off, start the Mini, then start the HD, the HD does not mount. Use the Disk Utility, the HD is gray out but will mount.

Reboot the Mini with the HD left on so that it starts up with the Mini, it will not mount, but the HD is grayout in the Disk Utility, and if mount is tried, an error is created.

Any suggestions?

Todd