Lost disc for Elements 6 so can't install on new laptop

If you can find your cd disc elements 6 will work on win 10.

If you own a more recent version then you might be able to find a download for it - version 7 and up is available for PSE.  If the other installation is still active then you could possibly acquire its serial number from the machine.

PSE 10, 11, 12, 13, 14, 15 - https://helpx.adobe.com/photoshop-elements/kb/photoshop-elements-downloads.html

PSE 7, 8, 9 - https://helpx.adobe.com/photoshop-elements/kb/photoshop-elements-7-8-9-downloads.html

PE 10, 11, 12, 13, 14, 15 - https://helpx.adobe.com/premiere-elements/kb/premiere-elements-downloads.html

PE 9 - https://helpx.adobe.com/premiere-elements/kb/premiere-elements-9-downloads.html

As far as finding the serial on the machine....

If it's a Windows machine then try running Belarc Advisor

http://www.belarc.com/free_download.html

For a Mac you can try: 

https://mac-product-key-finder.com/

https://forums.adobe.com/thread/2174645   shows how to find it directly...

    If you are on a Mac navigate to:

    Macintosh HD >> Library >> Application Support >> regid.1986-12.com.adobe

    Inside the folder “regid.1986-12.com.adobe” you will probably find several files ending .swidtag

    For example: regid.1986-12.com.adobe_DesignSuitePremium-CS5-Mac-GM-en_US.swidtag

    Look for the one related to your product and right-click (control-click) on it and choose:

    Open With >> Other

    Then choose TextEdit from the list of applications.

    For registered products the 24 digit serial number is usually found near the bottom of the text document.

    On Windows navigate to:

    C:\ProgramData\regid.1986-12.com.adobe

    Open in Note Pad

Mac Product Key Finder. Recover lost product keys for Mac applications (https://mac-product-key-finder.com/)

Recovering CS6 serial numbers requires purchasing the Pro version for $30.

Their website says it only works on OS X up to Yosemite - not El Capitan yet.

Elements 6 (Both Photoshop and Premiere) is not available.  Even if it was it is highly doubtful it could install/run in Windows 10.  Your only option is to purchase the latest version, though you should be able to get it at an upgrade price as long as you still have the serial number for 6.