Q:

Laravel 404 Not Found

I have a problem with "404 | Not found".  The route exists, but I still have the problem. 
I've already tried with:
php artisan route:list

and the route really exists. 
web.php:
Route::get('/', function () {
    return view('welcome');
});

Auth::routes();

Route::get('/p/create', 'PostsController@create');
Route::get('/p/{post}', 'PostsController@show'); 
Route::post('/p', 'PostsController@store');

Route::get('/profile/{user}', 'ProfilesController@index')->name('profile.show');
Route::get('/profile/{user}/edit', 'ProfilesController@edit')->name('profile.edit'); //this shows the form of edit profile
Route::patch('/profile/{user}', 'ProfilesController@update')->name('profile.update'); //this will actually do the process of updating our profile

ProfilesController.php:
public function edit(User $user)
{
    return view('profiles.edit', compact('user'));
}

public function update(User $user){ //some validation
        $data =request()->validate([
            'title' => 'required',
            'description' => 'required',
            'url' => 'url', //require the http://
            'image' => '',
        ]);

        auth()->user()->profile->update($data); //auth() is a protection.  Without this, an external user, for example in incognite, can edit the profile
    }

edit.blade.php:
@extends('layouts.app')

@section('content')
<div class="container">
<form action="/profile->{{ $user->id }}" enctype="multipart/form-data" method="POST">
        @csrf
        @method('PATCH') <! --it's not permitted write method = 'patch', by default it will be get-->
            <div class="row">
                    <div class="col-8 offset-2">

                        <div class="row">
                            <h2>Edit Profile</h2>
                        </div>
                        <div class="form-group row">
                            <label for="title" class="col-md-4 col-form-label">Title</label>
                                    <input id="title"
                                           type="text" 
                                           class="form-control @error('title') is-invalid @enderror"  
                                           name="title"
                                           value="{{ old('title') ??  $user->profile->title }}" 
                                           autocomplete="title" autofocus>

                                    @error('title')
                                        <span class="invalid-feedback" role="alert">
                                            <strong>{{ $message }}</strong>
                                        </span>
                                    @enderror
                            </div>

index.blade.php:
@extends('layouts.app')

@section('content')
<div class="container">
    <div class="row">
        <div class="col-3 p-5">
            <img src="https://scontent-fco1-1.cdninstagram.com/vp/1ba68a1705bb9cdd1f7f2ea9ea062810/5D79BFC8/t51.2885-19/s320x320/22709172_932712323559405_7810049005848625152_n.jpg?_nc_ht=scontent-fco1-1.cdninstagram.com" style = "height:150px" class = "rounded-circle">
        </div>
        <div class="col-9 pt-5">
            <div class="d-flex justify-content-between align-items-baseline">
                <h1>{{ $user -> username}}</h1>
                <a href="/p/create">Add New Post</a>
            </div>
            <a href="/profile/{{ $user->id }}/edit">Edit Profile</a>
            <div class = "d-flex">
            <div class = "pr-5"><strong>{{ $user->posts->count() }}</strong> posts</div>
                <div class = "pr-5"><strong>23k</strong> followers</div>
                <div class = "pr-5"><strong>212</strong> following</div>
            </div>  
        <div class = "pt-4 font-weight-bold">{{ $user->profile->title }}</div> 
        <div>{{ $user->profile->description }}</div> 
        <div><a href="#">{{ $user->profile->url }}</a></div>
        </div>
    </div>
    <div class="row pt-5">
        @foreach($user->posts as $post)
            <div class="col-4 pb-4">
            <a href="/p/{{ $post->id }}">
                <img src="/storage/{{ $post->image }}" class = "w-100">
            </a>
            </div>
        @endforeach
    </div>
</div>
@endsection

The error is only "404 | Not Found".  When I click the button for edit the address became: "http://localhost:8000/profile->1" and the error is probably there. 

A:

Fistly the issue is you're generating an invalid URL.  
/profile->{{ $user->id }} will generate /profile->1 but -> must not be part of the URL.  Normally you could fix this by just doing /profile/{{ $user->id }}. 
However I suggest you should use Laravel's URL generator helpers to generate URLs. 
For example: <form action="/profile->{{ $user->id }}" should be:
<form action="{{ route('profile.update', [ 'user' => $user->id ])}}"

As a reminder there's 3 major route helpers:
url('/relative/path'); // Will generate an absolute URL to your app based on a relative URL
action('Controller@action'); // Will generate a URL which calls the specified controller 
route('route.name'); // Will generate a URL based on the named route

The second parameter in route will fill in required route parameters.