Is the problem in the view or in the Controller? Your code is quite confused; you are creating a record in an update method; we would typically use the store method; which does not need an existing ID:
<form class="form" action="{{ route('admin.finance.store') }}" method="POST">
public function store(Request $request)
There is no file uploaded (based on the validation rules), so the enctype attribute is unnecessary; also the @method('PUT') is unnecessary if you use the convention store` action:
Why are you expecting a Finance $finance parameter and $id in the update method??? If you are Route-Model Binding, then
Route::put('/finances/{finance}, [FinanceController::class, 'update'])->name('admin.finance.update');
public function update(Request $request, Finance $finance)