When would you use the protected internal and internal access modifier?

Protected - If you need to protect any data or you need to protect any of your method from out side access, keep it inside protected class. Epecially using when you are delivering any 3rd party library. Your library may contain logics handlings different clients. So you need to ensure that one client not touching classes meant for other clients.
eg:-

// Assembly1.cs
// compile with: /target:library
internal class BaseClass 
{
   public static int intM = 0;
}

// Assembly1_a.cs
// compile with: /reference:Assembly1.dll
class TestAccess 
{
   static void Main() 
   {
      BaseClass myBase = new BaseClass();   // Compile erro will get.
   }
}

Protected Internal


Access is limited to the current assembly or types derived from the containing class.
Eg:-
Assembly1 class- 
public class Class1
    {
        protected internal void Class1Test()
        {
        }
    }
Assembly2 class
class Class3 : Class1
    {
        private void Test()
        {
            Class3 clss = new Class3();
            clss.Class1Test();
        }
    }
As you can see, if yu want to ensure a class member accebility through it's inherit class only, use this pattern