cSharpFunction

public class StringAppend
	{
		public delegate void StringOverflow(object sender, int Overflow);
		public event StringOverflow StringOverflow_EventHandle;

	}
  
  
  class Program
{
	 void Main(string[] args)
	{
		StringAppend sa = new StringAppend();
		sa.StringOverflow_EventHandle += new StringAppend.StringOverflow(string_over);
                sa.StringOverflow_EventHandle += string_over;
		sa.StringOverflow_EventHandle += (sender, Overflow) => { };
		sa.StringOverflow_EventHandle += delegate {
			
		};
	}

	private void string_over(object sender, int num_over)
	{ 
	
	}
}

line 15 your handler is in StringAppend class. Therefore you need to create object of that class first and then use the handler method.
you can rewrite something like this.

var stringAppend = new StringAppend();
sa.StringOverflow_EventHandle += stringAppend.StringOverflow(string_over);

but for line 16 that handler method is in a class therefore you don't need to create new object, just use method directly in optional you can use this keyword.

 16           sa.StringOverflow_EventHandle += this.string_over;