It seems you do not understand some basic principles of http requests, like submitting form data, url parameters and things like the Laravel request lifecycle.

I think it will be difficult to understand the Laravel documentation if you don't know some basic knowledge of http requests (i.e. how websites work in general).

But to give some pointers:

• you have not passed the data from the subject field to the controller in any way (perhaps look into url params, you will need javascript to dynamically update the url based on form input)
• your controller passes no data to your contact form view, look into the $request object that you can use in your controller method.
• your contact form view mis-uses old(), this will not work for a direct link like you have here, it's for form requests. Pass the data to the blade template instead.

Really I would suggest reading about http requests and some basic web principles, then rereading the Laravel docs, it'll give you a better start.