Microsoft tries so hard to make things simple, yet often winds up making them harder.
I needed to set folder permissions with an ASP.Net 4.0 website running on Server 2012.   The problem was the site worked, but certain folders needed Modify rights.
To make this happen properly, you have to:
1.  Locate the name of the application pool assigned to your asp.net website.  In my case, we’ll call it BlahAppPool.  You can find which app pool is assigned by using IIS Manager and going to the Basic Settings of the website in question.
2.  Now that you know the name of the app pool, the trick to setting folder permissions in Server 2012…
You must add the credentials as IIS APPPOOL\BlahAppPool
You won’t see it listed if you do a search.  It’s a virtual account.  Every app pool gets a virtual account in Server 2012.  And make sure you have the space between IIS and APPPOOL.
Once you get it added, now you can check the Modify right and save.   You remembered to propagate permissions to child objects didn’t you?