I am trying to call to a Web API from MVC POST action method and receive a result but not sure how, for example:
    [HttpPost]
    public ActionResult Submit(Model m)
    {
        // Get the posted form values and add to list using model binding
        IList<string> MyList = new List<string> { m.Value1,
                m.Value2, m.Value3, m.Value4};
        return Redirect???? // Redirct to web APi POST
        // Assume this would be a GET?
        return Redirect("http://localhost:41174/api/values")
    }
I wish to send the above MyList to the Web Api to be processed, then it will send a result (int) back to the original controller:
// POST api/values
    public int Post([FromBody]List<string> value)
    {
        // Process MyList
        // Return int back to original MVC conroller
    }
Have no idea how to proceed, any help appreciated.
You shouldn't redirect with POST, a redirect almost always uses GET, but you don't want to redirect to an API anyway: what is the browser going to do with the response?
You'll have to perform the POST from your MVC controller and return the data.
Something like this:
[HttpPost]
public ActionResult Submit(Model m)
{
    // Get the posted form values and add to list using model binding
    IList<string> postData  = new List<string> { m.Value1, m.Value2, m.Value3, m.Value4 };
    using (var client = new HttpClient())
    {
        // Assuming the API is in the same web application. 
        string baseUrl = HttpContext.Current
                                    .Request
                                    .Url
                                    .GetComponents(UriComponents.SchemeAndServer, UriFormat.SafeUnescaped);
        client.BaseAddress = new Uri(baseUrl);
        int result = client.PostAsync("/api/values", 
                                      postData, 
                                      new JsonMediaTypeFormatter())
                            .Result
                            .Content
                            .ReadAsAsync<int>()
                            .Result;
        // add to viewmodel
        var model = new ViewModel
        {
            intValue = result
        };
        return View(model);
    }           
}
                        Your Web API controller shouldn't be doing much itself. In an application that has proper Separation of Concerns, your processing should be done elsewhere. For example:
This might be in your domain model.
public class StringUtilities
{
    //Just a representative method of one way of processing the strings
    public int CountSomeStrings(IEnumerable<string> strings)
    {
        return strings.Count();
    }
}
Part of your Web API
// POST api/values
public int Post([FromBody]List<string> value)
{
    return StringUtilities.CountSomeStrings(value);
}
Then calling in your MVC controller, no need to call the Web API. Just call the method it calls directly.
[HttpPost]
public ActionResult Submit(Model m)
{
    // Get the posted form values and add to list using model binding
    IList<string> MyList = new List<string> { m.Value1,
            m.Value2, m.Value3, m.Value4};
    int NumStrings = StringUtilities.CountSomeStrings(MyList);
    ViewBag["NumStrings"] = NumStrings;
    return View();
}
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