What did you mean with "how to do it with my request?". Values in Request object are about your clients coming to your site. Do you want to make a server side request to a URL?
If you want to make a server side request you can put value to :
WebRequest request = WebRequest.Create("domain.com");
request.ContentType = "application/xxx; charset=utf-32";
request.GetResponse();
Edit:
The values in the Request are determined by clients that request your URL. In the page you share, there is a requestEncoding attribute. But the description of the attribute says that it specifies assumed encoding. But it is clear that any request having Accept-Charset in its Header, simply override your setting. By the way, building any architecture belongs requestEncoding setting is not recommended. If you are developing a multiuser or public application, you may not decide how Request shaped.
You can also do it with UploadData method of WebClient:
WebClient wc = new WebClient();
wc.Headers.Add("Content-Type", "application/x-www-form-urlencoded; charset=utf-8");
byte[] responseArray = wc.UploadData("URL_TO_POST", System.Text.Encoding.Default.GetBytes("param1_name=param1_value¶m2_name=param2_value"));
string responseText = System.Text.Encoding.ASCII.GetString(responseArray);