There might be a place in Acrobat to look at System Information and maybe that lists your serial number. I don’t have Acrobat so I’m not sure.
Otherwise, there is a program called Belarc Advisor that can find serial numbers for various products, including at least some from Adobe and it might work for you:
And if you register your Acrobat with Adobe, perhaps the serial number is listed at www.adobe.com under your My Adobe or My Products areas you can get to by hovering your mouse over your name at the top right.
Thank you very much! I appreciate the assistance.