You don't need to make a call to a geometry service if you are projecting lat/long to or from Web Mercator. The WebMercatorUtil class does this for you. Here's another version of Shuping's code
<?xml version="1.0" encoding="utf-8"?>
<s:Application xmlns:fx="http://ns.adobe.com/mxml/2009"
xmlns:s="library://ns.adobe.com/flex/spark"
xmlns:esri="http://www.esri.com/2008/ags"
pageTitle="World Street Map" xmlns:mx="library://ns.adobe.com/flex/mx">
<fx:Script>
<![CDATA[
import com.esri.ags.Graphic;
import com.esri.ags.SpatialReference;
import com.esri.ags.events.GeometryServiceEvent;
import com.esri.ags.events.MapEvent;
import com.esri.ags.geometry.Geometry;
import com.esri.ags.geometry.MapPoint;
import com.esri.ags.symbols.SimpleMarkerSymbol;
import com.esri.ags.utils.WebMercatorUtil;
import mx.controls.Alert;
protected function map1_loadHandler(event:MapEvent):void
{
//project the lat and long values from 4326 to 102100
var myPoint:MapPoint = new MapPoint(-122, 73, new SpatialReference(4326));
// geometryService.project([myPoint as Geometry], new SpatialReference(102100),null);
var myGraphic:Graphic = new Graphic(WebMercatorUtil.geographicToWebMercator(myPoint), new SimpleMarkerSymbol(SimpleMarkerSymbol.STYLE_DIAMOND, 22, 0x009933));
myGraphicsLayer.add(myGraphic);
map.centerAt(myGraphic.geometry as MapPoint);
}
// protected function geometryService_projectCompleteHandler(event:GeometryServiceEvent):void
// {
// var pt:MapPoint = (event.result as Array)[0]as MapPoint;
// var myGraphic:Graphic = new Graphic(pt, new SimpleMarkerSymbol(SimpleMarkerSymbol.STYLE_DIAMOND, 22, 0x009933));
// myGraphicsLayer.add(myGraphic);
// map.centerAt(pt);
// }
]]>
</fx:Script>
<fx:Declarations>
<esri:GeometryService id="geometryService"
projectComplete="geometryService_projectCompleteHandler(event)"
url="http://sampleserver3.arcgisonline.com/ArcGIS/rest/services/Geometry/GeometryServer"/>
</fx:Declarations>
<esri:Map id ="map" load="map1_loadHandler(event)">
<esri:ArcGISTiledMapServiceLayer url="http://server.arcgisonline.com/ArcGIS/rest/services/World_Street_Map/MapServer"/>
<esri:GraphicsLayer id="myGraphicsLayer"></esri:GraphicsLayer>
</esri:Map>
</s:Application>