Routing: The current request for action [...] is ambiguous between the following action methods

You can only have a maximum of 2 action methods with the same name on a controller, and in order to do that, 1 must be [HttpPost], and the other must be [HttpGet].

Since both of your methods are GET, you should either rename one of the action methods or move it to a different controller.

Though your 2 Browse methods are valid C# overloads, the MVC action method selector can't figure out which method to invoke. It will try to match a route to the method (or vice versa), and this algoritm is not strongly-typed.

You can accomplish what you want using custom routes pointing to different action methods:

... in Global.asax

routes.MapRoute( // this route must be declared first, before the one below it
     "StartBrowse",
     "Gallery/Browse/Start/Here",
     new
     {
         controller = "Gallery",
         action = "StartBrowse",
     });

routes.MapRoute(
     "ActualBrowse",
     "Gallery/Browse/{searchterm}",
     new
     {
         controller = "Gallery",
         action = "Browse",
         searchterm = UrlParameter.Optional
     });

... and in the controller...

public ActionResult Browse(string id)
{
    var summaries = /* search using id as search term */
    return View(summaries);
}

public ActionResult StartBrowse()
{
    var summaries = /* default list when nothing entered */
    return View(summaries);
}

You might also be able to keep the action methods named the same in the controller, by applying an [ActionName] attribute to one to distinguish it. Using the same Global.asax as above, your controller would then look like this:

public ActionResult Browse(string id)
{
    var summaries = /* search using id as search term */
    return View(summaries);
}

[ActionName("StartBrowse")]
public ActionResult Browse()
{
    var summaries = /* default list when nothing entered */
    return View(summaries);
}

I don't know when the question was asked this solution was available but you can use:

Request.QueryString["key"]

So this should work fine for your problem:

[HttpGet]
public ActionResult Browse()
{
    if( Request.QueryString["id"] != null )        
        var summaries = /* search using id as search term */
    else /*assuming you don't have any more option*/
        var summaries = /* default list when nothing entered */

    return View(summaries);
} 

Add following code in RouteConfig.cs before Default route

routes.MapMvcAttributeRoutes();

And add route attributes in the controller like:

    [Route("Cars/deteals/{id:int}")]
    public ContentResult deteals(int id)
    {
        return Content("<b>Cars ID Is " + id + "</b>");
    }

    [Route("Cars/deteals/{name}")]
    public  ContentResult deteals(string name)
    {
        return Content("<b>Car name Is " + name + "</b>");

    }