You are using incorrect overload. You should use this overload
public static MvcHtmlString ActionLink(
this HtmlHelper htmlHelper,
string linkText,
string actionName,
string controllerName,
Object routeValues,
Object htmlAttributes
)
And the correct code would be
<%= Html.ActionLink("Create New Part", "CreateParts", "PartList", new { parentPartId = 0 }, null)%>
Note that extra parameter at the end.
For the other overloads, visit LinkExtensions.ActionLink Method. As you can see there is no string, string, string, object
overload that you are trying to use.