How to solve problem with root in ubuntu and need to change images from website?

Question

ubuntu

I'm trying to upload images to the admin panel as in this video https://youtu.be/EgjHlT_ExSw?t=17m2s gives the same error, but nothing changes when changing write permissions, there may be some other reasons for this error.
Project - the projects model

<?php namespace App;

use Illuminate\Database\Eloquent\Model;

class Project extends Model {

  protected $table = 'projects';

    public function galleries()
    {
        return $this->hasMany('\App\Gallery');
    }
}

<?php
return [
    'title' => 'Projects',
    'single' => 'project',
    'model' => '\App\Project',
    'columns' => [
        'id',
        'active',
        'title'
    ],
    'edit_fields' =>[
        'active' =>[
            'type' => 'bool'
        ],
        'title' => [
            'type' => 'text'
        ],
        'slug' => [
            'type' => 'text'
        ],
        'content' => [
            'type' => 'wysiwyg'
        ],
        'image' => [
            'type' => 'image',
            'location' => public_path().'/uploads/project/original',
            'sizes' => [
                [500, 500, 'auto', public_path().'/uploads/project/medium/', 100],
                [1000, 800, 'auto', public_path().'/uploads/project/large/', 100]
            ]
        ]
    ],
    'form_width' => 800,
];

If you remove the lines

'sizes' => [
                [500, 500, 'auto', public_path().'/uploads/project/medium/', 100],
                [1000, 800, 'auto', public_path().'/uploads/project/large/', 100]
            ]
        ]

then the image is loaded but not sliced.
UPD1
config file of another menu item where everything loads fine

<?php

return [
    'title' => 'Slides',
    'single' => 'slide',
    'model' => '\App\Slider',
    'columns' =>[
        'id',
        'active',
        'image' =>[
            'output' => '<img src="/uploads/slides/small/(:value)" />'
        ]
    ],
    'edit_fields' =>[
        'active' =>[
            'type' => 'bool'
        ],
        'weight' => [
            'type' => 'number'
        ],
        'image' => [
            'type' => 'image',
            'location' => public_path().'/uploads/slides/original/',
            'sizes' => [
                [100, 100, 'auto', public_path().'/uploads/slides/small/', 100],
                [1000, 800, 'auto', public_path().'/uploads/slides/large/', 100]
            ],
        ]
    ]
];

Answer 1

Perhaps you should assign a different owner? For example on apache:apache?