Read this:
ASP.Net MVC – How to create a ListBox?[
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Here on Index method, you'd be getting the selected value from the listbox. Instead here, store your selected value in ViewBag and load that value in the view for the textbox.
Another approach is, bind the selected value to the model and pass it to the view. And use
@Html.TextBoxFor()
to render the value.
-KR