submit data by js onclick event in Laravel

As far as I know you should not have more than one tag in a view. I suggest you use ajax to trigger the submit event. However, you don't even have one form open tag but just a a checkbox.

I might need some more information but from what I understand you need to submit data to the controller when the checkboxes are clicked.

I would do it this way:

// Your view
<!-- CSRF Token -->
    <input type="hidden" name="_token" value="{{{ csrf_token() }}}" />
<!-- ./ csrf token -->

@foreach ($items as $item)
<input type="checkbox" name="{{$item->id}}" id="{{$item->id}}" value="{{$item->done}}" class="checkbox_click">
@endforeach

<script type="text/javascript">
    $(document).ready(function() {
        $('.checkbox_click').click(function(){                  
            var currentValue = $(this).attr("value");
            $.ajax({
                url: 'your/route',
                method: 'post',             
                data: {id: currentValue, _token: $('input[name="_token"]').val()},
                success: function(data){
                    alert(data);
                },
                error: function(){},
            });
        });         
    });
</script>

// Your controller
public function postIndex()
{
    if (Request::ajax)
    {
        $id = Input::get('id');

        return Response::json($id);
    }
}

// Your routes.php
Route::post('your/route', YourController@postIndex);