As you seem to be on a learning exercise I suggest you do the following
-
create a resourceful route: https://laravel.com/docs/5.4/controllers#resource-controllers
-
run
php artisan route:listto see which routes have been created
You will get a list like this:
POST | tasks | tasks.store
GET|HEAD | tasks | tasks.index
GET|HEAD | tasks/create | tasks.create
DELETE | tasks/{task} | tasks.destroy
PUT|PATCH | tasks/{task} | tasks.update
GET|HEAD | tasks/{task} | tasks.show
GET|HEAD | tasks/{task}/edit | tasks.edit
So to delete a task you would send a DESTROY request to the route tasks/{task}
This is what is probably called very common setup on what request types you run on what kind of route structure.
To achieve this your button would need to be a FORM, not only a link like in your setup (a link will send a GET request)
Of course you can also creaste a setup where the GET call triggers the delete action but that is not standard.
Tip: You probably should consider to use blade syntax instead of php in your view. There are @foreach, @if and so on that clean up your code dramatically.