Part 1 step 1 - 12
https://transparentgov.net/cleargov1/1795/how-find-organizations-portal-server-everything-arcgis-part
Step 11.
rcpc is their arcgis online organization short name, this has big use, you can now know their organization's home page url:
[organization-short-name] + [.maps.arcgis.com]
rcpc.maps.arcgis.com
https://rcpc.maps.arcgis.com/home/index.html

Step 12.
organization's home page url is what you get when you pay ESRI $50,000 per year !!!!!
organization's home page url:
[organization-short-name] + [.maps.arcgis.com]
You actually paying $50k per year for your [organization-short-name]
All ESRI licensing now through this [organization-short-name].
Old time, we use arcMap license manager.
But now, Arcgis Pro time, ArcPro license by you log in your organization home page which is [organization-short-name] + [.maps.arcgis.com]
From here, you can clearly see their organization full name
https://rcpc.maps.arcgis.com/home/index.html

Step 13.
If you want to find this organization's all layers, all maps, etc.... everything, click 'gallery' tab
https://rcpc.maps.arcgis.com/home/index.html

Step 14.
click layer tab, will reveal all layers this orgnization have.
https://rcpc.maps.arcgis.com/home/gallery.html?sortField=relevance&sortOrder=desc&focus=layers
now click any layer you like

Step 15.
click any layer, you can find this organization's self hosted Arcgis enterprise portal (Arcgis server URL), all their self hosted layer is there.( not host on esri.com, not paying esri, physically store on their server room hard drive).
https://rcpc.maps.arcgis.com/home/gallery.html?sortField=relevance&sortOrder=desc&focus=layers
gis.rcgov.org
is their self hosted arcgis enterprise portal

Step 16.
From last step, you recovered one of their layer's arcgis rest api endpoint ( on self hosted enterprise portal)
https://gis.rcgov.org/arcgiswebadaptor/rest/services
Now you click home will reveal you their federated arcgis server root folder ( self hosted enterprise arcgis server root folder )
gis.rcgov.org
is their self hosted enterprise portal domain in internet.
arcgiswebadaptor
by default, is "arcgis", when you install IIS web adaptor, if you don't change anything, just click next, next, this value default to "arcgis", that is why you see 90% of organization use default value 'arcgis'.
This organization admin maybe not well understand what this value should be, when he install IIS web adaptor, he just over worry about what should type in this value, so he endup type arcgiswebadaptor, which is ok, results him in 10% of people who don't use arcgis as default value. But you need to understand why and what happen in such case.

Step 17.
By knowing enterprise portal domain, gis.rcgov.org
By default, enterprise portal home page should be:
https://[portal-domain]/portal/home/index.html
https://gis.rcgov.org/portal/home/index.html
You get error, obviously this organization gis admin don't use default portal web adaptor

Step 18.
This organization version is 10.51, my guess, is that it is too old, now is v11.2. 10.51 maybe not have a federated server yet, maybe not have portal yet, or even have portal, it setup differently from current v11.2. To find out, you need to log into their enterprise portal server, to looking for 'portal web adaptor' in IIS manager. Portal adaptor name will list there along with above arcgiswebadaptor

Step 19. summary see part 3
https://transparentgov.net/cleargov1/1797/how-find-organizations-portal-server-everything-arcgis-part