can i burn dvd's in my Mac with Big Sur 11.4? I have an external drive for CD's.

Yes. To create and burn a video DVD you'll need a video DVD authoring application. There are many to choose from at the App Store. Many have demo versions you can try before purchasing. They put a watermark on the output presentation which is removed from the purchased version.

Updated to Big Sur 11.4 las night and now from the previous version and now it doesn't recognise my external DVD/CD burner. I just used it before the OS update and it was working then in the previous release of Big Sur. Restarting, disconnecting and reconnecting doesn't help. Disk Utility can't even find the drive when it is running with a dvd inside. Really disappointed in the new update. I've used this drive since I bought my Macbook Pro mid 2014 and I have never had any problems before. I used the drive just seconds before I updated to Big Surf 11.4.

Note: It could aslo be that Big Sur 11.4 doesn't support my Elgato thunderbolt 2 dock. Since it is discontinued, there are no software updates anymore, but it was working with the previous version of Big Sur 11.3.

As I wrote in the above, I did not change any of my previous settings. Yes, all boxes are ticked, as they have been for years. Yes, I inserted a DVD in the drive. As I wrote in the above, it worked per usual, the way I have been using it for the past 8 years, until the latest upgrade. But now I suspect it’s due to my thunderbolt 2 dock. I’ve had it for many years and the drive have worked fine with it (and worked just seconds before I started the upgrade) but after the upgrade it doesn’t work. All the settings are enables as before the upgrade (it would be strange if the upgrade had changed the preferences I’ve had for years) and the drive isn’t even discovered by disk utility, no matter how many DVD’s or empty DVDs’ I’ve tried. Something major seems to change between 11.3 and 11.4 since it literally worked per usual just seconds before I upgraded and minutes after the upgrade it can’t discover the drive in disk utility, despite a dice running in the drive and the settings to view all external disks, CD,DVD, iPods.

Do you have this checkbox selected in the Finder's General preference pane?

and then it won't show unless you have a disc in the drive.

Are you able to use the optical drive if it's plugged directly into the iMac?