remoteShaedObject is used to exchange data on the clients connected.
First you need to connect to FMS sever and then ceate sharedObject and attach a function to syncEvent.
Say you have to draw a shape line, in that case you should store the string containing line properties( color,thickness, x, y, startX ,endX) to shared Object. When you add it to your shared object it will trigger the sync event on all the connected users. And you will receive these properties in the attached listener function to sync event. Now you can use this data to create line on all the users connected.

very very thanks for your reply Dave.
now I am able to draw a single line and it will display on another shared screen.

1>But application is giving error at initlilze of null object reference as no object passed at initilize. how to overcome i??

2> whenever I draw a curve by mouse pointer a straight line again joines the 2 points, means 2 line gets drawn i> curve ii>straight line btwn 2 points

3>on the other screen the line is getting drawn bt not at same coordinates.

4> I am struggling with a multiple line objects passing to the FMS. and a for loop to retrieve it in sync it.
pls help me so that i can complete my line part and go for circle

I am posting my code here


<?xml version="1.0" encoding="utf-8"?>
<mx:Application xmlns:mx="http://www.adobe.com/2006/mxml" layout="absolute" minWidth="955" minHeight="600" initialize="init();">
<mx:Script>
<![CDATA[
import flash.display.CapsStyle;
import flash.display.JointStyle;
import flash.display.LineScaleMode;
import flash.display.Shape;
import flash.display.Sprite;

import mx.containers.Canvas;
import mx.controls.Alert;
import mx.core.UIComponent;
import mx.utils.ObjectUtil;

private var _canvas:Canvas;
private var allowDrawing:Boolean=false;

private var _startX:Number;
private var _startY:Number;
private var _endX:Number;
private var _endY:Number;
private var _netConnection:NetConnection;
private var _remoteSO:SharedObject;


private function init():void
{
_canvas = new Canvas();

this.addEventListener(MouseEvent.MOUSE_DOWN,mouseDownHandler);
this.addEventListener(MouseEvent.MOUSE_UP, mouseUpHandler);
this.addEventListener(MouseEvent.MOUSE_MOVE,mouseMoveHandler);
this.addChild(_canvas);


_netConnection = new NetConnection();
_netConnection.addEventListener(NetStatusEvent.NET_STATUS,netStatusHandler);

//--------"whiteboard" folder created at FMS in applications folder
_netConnection.connect("rtmp:/whiteboard");


}

private function netStatusHandler(event:NetStatusEvent):void
{
switch (event.info.code)
{
// Successful connection to the server
case "NetConnection.Connect.Success" :
createARemoteSO() ;
break ;
}
}

private function createARemoteSO():void
{
//
_remoteSO = SharedObject.getRemote("drawing_whiteboard",_netConnection.uri,false);
_remoteSO.connect(_netConnection);


_remoteSO.addEventListener(SyncEvent.SYNC,drawLineHandler);
}

private function drawLineHandler(event:SyncEvent):void
{
var lineObj:Object= _remoteSO.data.line as Object;
_canvas.graphics.lineTo(lineObj.startX ,lineObj.startY );
_canvas.graphics.moveTo( lineObj.endX, lineObj.endY);


//here i get stuck in getting all lines object????????????????????????/

/* for each(var slot1:String in _remoteSO.data)
{
Alert.show(ObjectUtil.toString(_remoteSO.data[slot1]) )
} */
}


private function mouseDownHandler(mEvent:MouseEvent):void
{
_startX= mEvent.target.mouseX as Number;
_startY = mEvent.target.mouseY as Number;
_canvas.graphics.moveTo(_startX,_startY);
_canvas.graphics.lineStyle(5, 0x00000,1, false,CapsStyle.ROUND);
allowDrawing=true;
}

private function mouseMoveHandler(event:MouseEvent):void
{
if(allowDrawing)
{
_endX=event.target.mouseX as Number;
_endY=event.target.mouseY as Number;
_canvas.graphics.lineTo(_endX,_endY);
event.updateAfterEvent();
}

}

private function mouseUpHandler(event:MouseEvent):void
{
allowDrawing = false;
var lineObject:Object = new Object();
lineObject.startX= _startX;
lineObject.startY= _startY;
lineObject.endX = _endX;
lineObject.endY =_endY;

//what for multiple line or drawing?????????????????????????/

_remoteSO.setProperty("line", lineObject as Object);
_canvas.clearStyle(null);


/* var slot:Object = "line_" + _startX + "-" + _startY + "X" + _endX + "-" + _endY;
_remoteSO.data[slot] = lineObject;
//sthis.removeEventListener(MouseEvent.MOUSE_MOVE,mouseMoveHandler);
*/
}



]]>
</mx:Script>
</mx:Application>

Check this link

http://www.jamesward.com/2006/08/16/flex-paint-flex-display-object-to-png/