While ActionScript 3.0 comes with the TextLineMetrics Class that allows you to get all kinds of information about a text selection, with Flash 8 and below you have to go all the way on your feet if you want to know the width or position of a line of text within a textfield.

Before Flash 8 the only way I know of to accomplish this was to split the whole text into single words and add up their widths. But Flash 8 offers a new way to do this which works by using a BitmapData object together with the rarely used getColorBoundsRect() method. Check out the code and a demo here:

function getLineMetrics( textfield:TextField, skipEmptyLines:Boolean ):Array
{
	var rememberBorder:Boolean = textfield.border;
	textfield.border = false;
	
	var lineHeight:Number = textfield.getTextFormat().getTextExtent("W").textFieldHeight - 4;
	
	// _global.__lineMeasureMap is used in order to cope with the flash memory leak that happens with
	// bitmaps that get defined inside of functions
	var bm:BitmapData = _global.__lineMeasureMap = new BitmapData(textfield._width,lineHeight,true,0);
	var lines:Array = Array();
	
	for (var i=0; i < textfield._height; i+=lineHeight )
	{
		bm.draw( test, new Matrix(1,0,0,1,0,-(i+2)));
		var r:Rectangle = bm.getColorBoundsRect(0xff000000,0xff000000,true);
		if (!skipEmptyLines || r.width>0){
			r.x += textfield._x;
			r.y += textfield._y + i+2;
			lines.push( r);						
		}
		bm.fillRect( bm.rectangle, 0 );
		
	}
	textfield.border = rememberBorder;
	_global.__lineMeasureMap.dispose();
	return lines;
}

Download getLineMetrix.fla demo here.