What product did you purchase? Creative Coud apps do not have a serial number.
As Brad already mentioned, it's important to know what application or service you've paid for. If you have a perpetual license to Adobe Acrobat, you will have a serial number, and you should have received it when with your invoice or your receipt. If you have a subscription to Adobe Acrobat, then you don't need a serial number - the subscription is tied to your Adobe ID. When the installer or application asks you about the type of installation you have, you select trial/subscription and then log in with your Adobe ID.
If you only want to convert PDF documents to MS Word, it's also possible that you have a subscription to Adobe's ExportPDF service. In that case, there is also no serial number involved: This is an online service where you upload your PDF document to http://cloud.acrobat.com/exportpdf and then download the converted Word or Excel file. Again, all you need in this case is your Adobe ID.