add userID to create

I suggest you to try this

$user = User::create(['name'=>'Pardeep']);
$user->id

I want to add $user->id to product table.

the problem is the $user->id doesn't exist in request

Make id as a auto increment

How about this one:

$project= Project::create([
            'name' => request('name'),
            'price' => request('price'),
            'user_id' => auth()->id()
]);

try it

If you have setup the relation products in the user model, you dont need to set the key at all, Eloquent will do it for you;

 $product = $request->user()->products()
    ->create(request(['name', 'price']));