<?php

public function edit($id)
{
    // Fetch Article
    $article = News::findOrFail($id);

    // Fetch All Categories
    $categories = Category::all();

    return view('your-view', compact('article', 'categories'));
}

//HTML

<select name="" id="">
    @foreach ($cateries as $category)
        @if($category->id == $article->category_id)
            //SELECTED OPTION
        @else
            //NORMAL OPTION
        @endif
    @endforeach
</select>