Call to a member function format() on string

$date is a string, not a Carbon object. Therefore you cannot format() it.

If it has come from an eloquent model then you can add it to the $dates array so that it is automatically converted to Carbon

https://laravel.com/docs/5.6/eloquent-mutators#date-mutators

How are you getting $date here? Where does it come from?

'due_date' => $date->format('d/m/Y'),

Usually it would be $conference->date->format('d/m/Y'); since it's a property on the conference model.

like

$conference = Conference::find(1);
echo $conference->date->format('d/m/Y');

You must specify the dates values in your model:

protected $dates = [ 'date_1', 'date_2' ];

Later you can user Carbon