I don't think you can retrieve it. Probably the only record was on the DVD case.
Did you buy it online from Adobe? By visiting your account, you can get the number there.
Otherwise, if you have some proof of purchase, contact Customer Support and I think they can help you.
See www.grainge.org for RoboHelp and Authoring tips
Thanks for the suggestion. I didn't know about that program. I downloaded it and ran it and it did find several license keys on my system, not not RoboHelp. It also didn't find some other keys for some things I'm sure I have installed and have licenses for. Looking around inside Keyfinder, it has a list of supported programs that is pretty long but nothing from Adobe is on the list. But thanks, running this was interesting.
Adobe likes to "chop off" the last 4 digits of serial numbers for security purposes. The key finders, such as the one listed above, will generally search the registry for the serial number. This is one of the key locations that have had this "chopping" process applied. So, even if this app was able to find the serial number, it would not be the complete serial.
Peter is right. If you do not have the original CD/DVD case with the serial number printed on it, you will need to contact Adobe directly. Peter linked you to a document that tells you how to do this.