ASP.Net Filter Dropdown list items from multiple tables

There are multiple issues with your code.

First you cannot bind a <select> element to a collection of complex objects. A <select> posts back the value of its selected option (which will be an int assuming the Id property of Language is int).

Next the view in the model is FilterViewModel (and your generating form controls with name attributes based on those properties), but your posting back to a different model (App) which does not contain those properties so nothing would bind anyway.

Your adding a null label option ("Select Language") and if that were selected, it would post a null value which would cause your query to fail.

There are also some bad practices which I have noted below.

Your view model should be

public class AppsFilterVM
{
    public int? Language { get; set; }
    public int? Platform { get; set; }
    public IEnumerable<SelectListItem> LanguageOptions { get; set; }
    public IEnumerable<SelectListItem> PlatformOptions { get; set; }
    ...
    public IEnumerable <App> Apps { get; set; }
}

Its not clear what AgeGroups and ProductCodes are for so I have omitted them in the code above, and from your comments, I have assumed that the user can filter by either Language or Platform or both

The controller code would be

public ActionResult FilterApps(AppsFilterVM model)
{
    var apps = _context.Apps;
    if (model.Language.HasValue)
    {
        apps = apps.Where(x => x.LanguageId == model.Language.Value);
    }
    if (model.Platform.HasValue)
    {
        apps = apps.Where(x => x.PlatformId == model.Platform.Value);
    }
    model.Apps = apps;
    ConfigureViewModel(model);
    return View(model);
}

private void ConfigureViewModel(AppsFilterVM model)
{
    // populate the selectlists
    var languages = _context.Languages;
    var platforms = _context.Platforms
    model.LanguageOptions = new SelectList(languages, "Id", "Name");
    model.PlatformOptions = new SelectList(platforms , "Id", "Name");
}

Then in the view (note its making a GET, not a POST)

@model.AppsFilterVM
....
@using (Html.BeginForm("FilterApps", "Apps", FormMethod.Get))
{
    @Html.LabelFor(m => m.Language)
    @Html.DropdownListFor(m => m.Language, Model.LanguageOptions, "No filter")
    @Html.ValidationMessageFor(m => m.Language) 
    @Html.LabelFor(m => m.Platform)
    @Html.DropdownListFor(m => m.Platform, Model.PlatformOptions, "No filter")
    @Html.ValidationMessageFor(m => m.Platform) 
    <input type="submit" value="Filter" />
}
@foreach (var group in Model.AgeGroups)
{
    ....

There a a few other thing you should not be doing. Your giving both <select> elements the same id attribute which is invalid html (the DropDownListFor() method already generates a unique id based on the property name).

You should not submit a form based on the change event of a <select> Not only is it unexpected behavior, if a user uses the keyboard to navigate through options (e.g. using the arrow keys, or typing a character to go to the first option starting with that letter, then the form will be immediately submitted. In addition, the user might select an option from the 2nd dropdownlist first, which would immediately post before they have a chance to select the option in the first one. Allow the user to make their selections, check them, and then submit the form when they choose to.

Your view should not contain linq queries, and your grouping and ordering should be done in the controller before you pass the model to the view. Your Apps property should in fact be a view model containing a property for the group name, and a collection property for the Apps, (similar to the view models in your previous question) so that the view is simply

@foreach(var group in Model.AgeGroups)
{
    @group.Name
    foreach (var app in group.Apps)
    {
        @app.ProductCode
        @app.Name
        @app.Platform
    }
}

You should also consider using ajax to submit your form, which would call separate server method that returns a partial view of just the Apps, and update the DOM in the success callback, which would improve performance. For an example, refer Rendering partial view on button click in ASP.NET MVC.