Create or Save Products with Category

Good day. May I please be assisted. I would like to save products with the category. I have a Product Model and Controller and same with Cats. So far I am able to create categories and they are stored in my db. I am also able to create products but when I select a category it does not display the category..

Here is my model and controller

class Product extends Model
{
    protected $fillable=['name','description','title','image','price'];

    public function cats()
    {
        //
        return $this->belongsToMany('App\Cat');
    }
    
}



    public function create()
    {

        $cats = Cat::all();
        return view('admin.product.create',compact('cats'));
    }

    
    public function store(Request $request)
    {

        $this->validate($request,[
           'name'=>'required',
           'description'=>'required',
           'price'=>'required',
           'image'=>'image|mimes:png,jpg,jpeg|max:10000'
        ]);

        $product = new Product();

        $product ->name = $request->input('name');
        $product ->title = $request->input('title');
        $product ->description = $request->input('description');
        $product ->price = $request->input('price');
        $product ->image=$request->input('image');

        if($request->hasFile('image')) {
            $file = Input::file('image');
            //getting timestamp
            $timestamp = str_replace([' ', ':'], '-', Carbon::now()->toDateTimeString());

            $name = $timestamp. '-' .$file->getClientOriginalName();

            $product->image = $name;

            $file->move(public_path().'/images/', $name);
        }
        
        $product ->save();
        $product->cats()->sync($request->cats, false);
        Session::flash('flash_message', 'Service successfully added!');
        return redirect()->back()->with('success', 'Service Successfully Added');
      
    }