Problem to call the event

You're mixing client-side events with server-side events and controls.

That image element you have there is not a server-side control so it won't fire any server-side events.
Also, that onclick is expecting to find a javascript function called ite_click6 which you don't have.

So either handle the click on javascript or change the image element into a server-side control and handle the click with the proper OnClick server-side event.

Thanks. can I have the details to further call one code-behind event, within the javascript event below?

    <link rel="stylesheet" type="text/css" href="http://code.jquery.com/ui/1.10.3/themes/smoothness/jquery-ui.css" />
    <script type="text/javascript" src="http://code.jquery.com/jquery-1.9.1.js"></script>
    <script type="text/javascript" src="http://code.jquery.com/ui/1.10.3/jquery-ui.js"></script>
    <script type="text/javascript">
        function event2() {
            ...
        }
    </script>

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You can't just fire the event like that but you can call a method on your page via ajax for instance using jQuery.

What do you want to do when you call that server-side function?

To further call one other .aspx page within another browser window.

call one other .aspx page within another browser window

What does this mean?
Open another page in a new window?

The basics of jQuery and AJAX are shown in this article.  It uses PHP for the server side, but the principles would be equally applicable to any server-side scripting language.
https://www.experts-exchange.com/Programming/Languages/Scripting/JavaScript/Jquery/A_10712-The-Hello-World-Exercise-with-jQuery-and-PHP.html

greetings HuaMinChen, , I am not sure I understand what your problems are from what I can get reading through this. In your initial code you have  -
     <img src="..." onclick="ite_click6" />


so The EVENT you talk of is the user touching the image on their smart phone? ? is that right?

and you say you need to have this touch event open another tab in the phone browser that has a different asp page in it. I do not think that this needs any ajax, you just have to have your javascript   ite_click6() function to do this? ?

but maybe I do not really see what the end result is for your touch-click event for this image?

just remembered, if you only need to open a new tab-window for an image you might try something like -
    <a target="_blank" href="http://google.com" title="Google Search"><img src="googleIcon.jpg" /></a>

if you need to do more with some javascript variables or page elements, you can do an onclick function for the image

Ray/Alexandre/Slick,

Like what I originally asked, I only want to see one sample, that is calling either one Ajax event or code-behind event, upon one click to the image on the page.

Thanks. Within the WebMethod, is it possible for me to further direct to one other page like

Response.Redirect("http://192.168.168.1/Showite/Default.aspx");

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?

Not like that because you're not in the process of a page post-back.
What you can do is send the url as a reply to that ajax code and use window.location.href to perform the redirection on the client side.

public partial class _Default : Page 
{
  [WebMethod]
  public static string DoMyStuff()
  {
    return "http://192.168.168.1/Showite/Default.aspx";
  }
}

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$.ajax({
  type: "POST",
  url: "PageName.aspx/DoMyStuff",
  data: "{}",
  contentType: "application/json; charset=utf-8",
  dataType: "json",
  success: function(resp) {
    if(resp){
        window.location.href=resp;
    }
  }
});

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As a rough example it should work.

...I only want to see one sample, that is calling either one Ajax event or code-behind event, upon one click to the image on the page.

That is exactly what you would have found if you had read the article linked here:
https://www.experts-exchange.com/Programming/Languages/Scripting/JavaScript/Jquery/A_10712-The-Hello-World-Exercise-with-jQuery-and-PHP.html

This is a very common question and you're not the first to ask!  That's why we have an article system here at E-E.  If you just make a search of the articles you will find many useful descriptions and examples for the most common programming questions.

Calm down Ray :)

Although the article is fine for client-side, the server-side "code" doesn't resemble at all to anything he needed to write to make it work in ASP.net. So in my opinion your bold italic whatever "exactly" is a bit off... :)

As the code client-side is the same, and if you really want to push it that hard for solutions, a good update to that article would be to add the .net version of it.

Cheers!