Final Cut Pro X - Cannot create DVD because the specific device cannot be found

So open System Information > Disc Burning. Does your Mac see the burner?

Russ

The drives appear to be ok.

When exporting from FCP X you get to choose your destination. Do you see them both there?

FWIW it is usually better to choose "Hard Drive" instead as this saves an img file that you can keep and burn as many copies as you want right from the Finder

It's not what I meant but it will do. (FWIW, System Information can be accessed a multiple ways – one of which is Apple menu > About This Mac > System Report; there is a lot of useful info there.)

To your issue, what Luis said about saving a disc image to the computer. I gather you've tried to burn using both drives? It's certainly possible that a drive may be functioning OK while reading a disk, but not OK writing to it.

If you still have trouble in the Finder, disconnect the external drive and see whether that resolves it.

Good luck.

Russ