Had main desk top computer crash and need to reinstall purchase but have installed on a lap top - how can I reinstall?

You can activate your software on two computers.  If you need to install it on a third machine (because one of the first two crashed), then you need to https://helpx.adobe.com/contact.html to reset your activation count.

If you just want to reinstall it on one of the first two machines, then just reinstall and re-activate it with your serial number.