In this forum it is a recurring speech,
All versions of the ESXi product prior to version 7.0 are no longer supported, some well beyond the stage defined as "technical guidance", therefore, if you had not purchased a license, you are not entitled to download the product or its updates today. I'm sorry if by chance I wasn't very clear but the substance of things doesn't change.
Version 6.0 is out of support, it is very old, if your hardware is supported you could upgrade to 6.5 or 6.7.
Ideally you should use version 7.0 or 8.0 but this depends on your hardware compatibility.
For vSphere 6.5 and vSphere 6.7 versions, general support ends on October 15, 2022.
The technical guide for vSphere 6.5 and vSphere 6.7 is available until November 15, 2023.
This link from HP may help you
If you go to the downloads page, use the combo box to change the major version. Currently available are 8.0, 7.0, 6.7, and 6.5. Then you can select the VMware vSphere Hypervisor (ESXi) downloads page. From there you can select the minor version you want to download.
There are notes on the vSphere download page stating
"Customers who have purchased VMware vSphere 6.5 can download their relevant installation package from the product download tab below. Looking to upgrade from vSphere 5.x or vSphere 6.0? Visit the VMware vSphere Upgrade Center."
I will try to put it in these terms and maybe I'm wrong, all admitted but not granted, going here: https://customerconnect.vmware.com/downloads/#all_products and choosing "end of life product" having an "entitelment", the customer can download the vSphere (or other product) components it might need. In my case I can "go down" till ESXi5.1 for others it may be different.
What about it?