Usually the HP discs do not need a license key entered. However, in some circumstances, the software may require you to enter the product key. If you cannot read it, you will need to recover it using software. If you need to buy the recovery disks for your computer you can find them
http/www.recovery-disks.com/hp-pavilion-dv6-entertainment-notebook-pc.html
That website stocks the discs for most HP computers. We use them to buy cd sets when our customers lose theirs or we need to replace a set or provide them with a computer we're selling a customer.
HP Pavilion DV6 restore disks are easy to use and come with instructions. If you have any trouble, just ask and we will help you install them
Simply going into the computer settings as the other person above stated will not work. That is not actually a product key.
The software you can use is called key finder software. Such as magic jelly bean keyfinder. This should properly pull the key for you. Do not reinstall the system until you use this software to pull the key off. Additionally, I would try and use two different programs to make sure you get the same result. I have had it in the past give me a completely different key.