Hello cronellien,
Thanks for visiting Apple Support Communities. We understand that your Mac isn't detecting your external DVD writer. If you haven't already, restart your Mac and try the drive again. Restarting can resolve many odd issues: Log out, sleep, wake, restart or shut down your Mac
If that doesn't help, check the System Information area to see if the drive is detected there. To open System Information, press and hold the Option key and choose Apple menu > System Information. From there, choose the USB area on the left and look for the drive information on the right. Here's more details on System Information, just in case: About System Information on your Mac
If the drive isn't being detected there, check the USB ports on your Mac to make sure they're working with other devices. This will help to rule out the ports as being the issue. If no device is working in the USB ports, reset the System Management Controller (SMC) as that can help with power related issues: How to reset the SMC of your Mac
If you're still having trouble, let us know more:
- Has the drive ever worked on your Mac?
- Did you try with a different disc?
The more details you can provide the better.
Take care.