The caretIndex means the index of the point(caret) position.

import fl.controls.TextInput;
import fl.controls.Label;

var textfield:TextField = new TextField();
textfield.x = textfield.y = 100;
textfield.width = textfield.height = 100;
textfield.text = "blog.totusinfo.com";

addChild(textfield);
textfield.addEventListener(MouseEvent.CLICK, caretindex);

function caretindex(event:MouseEvent):void {

	var textfield:TextField = TextField(event.target);

	var myLabel:Label = new Label();
	myLabel.text = "Caret Index";
	myLabel.x = 10;
	myLabel.y = 10;
	addChild(myLabel);

	var textInput:TextInput = new TextInput();
	textInput.x = 75;
	textInput.y = 10;
	textInput.text = String(textfield.caretIndex);
	addChild(textInput);

}