I have an old Mac backup file and a new back up file. Trying to access the old one

I had a former Mac that died and they replaced it with a new one.  I have the old back-up file on my WD MyBookLive back-up drive and also the new backup file.  I’m trying to create more room on my back-up drive but before I delete the old backup I want to verify what is on there.  How can I access it from my newer mac?  I can’t figure out how to find it and open it.

Thank you.

Hello, what software did you used to create the backup?