Hey Billy,
Your PostsController is not inside the default namespace (which is Vanguard\Http\Controllers) and that's why you cannot use it like that. Your form open tag should look like following:
{!! Form::open(['action' => 'Web\PostsController@store', 'method' => 'POST']) !!}
However, I would recommend you to use named routes instead since using controller actions makes things too coupled. In general, your view files should not know how your controllers are organized and which methods should be triggered when a form is submitted. That's why you can use (named) routes to make a connection between a specific view, route, and a controller method.
Here you can learn more about named routes: https://laravel.com/docs/5.6/routing#named-routes
- Milos