To answer your specific question, you cannot have two methods with the same name and the same arguments in a single class; using the HttpGet and HttpPost attributes doesn't distinguish the methods.
To address this, I'd typically include the view model for the form you're posting:
public class HomeController : Controller
{
[HttpGet]
public ActionResult Index()
{
Some Code--Some Code---Some Code
return View();
}
[HttpPost]
public ActionResult Index(formViewModel model)
{
do work on model --
return View();
}
}