How to let the user create a selection of categories via the backend

Question

Consider this: I've got a custom post type 'portfolio' these posts, or "portfolio items" all have several categories such as: "photography", "concepting", "branding" , "clientA" , "clientB" etc.

Now I want to build a custom backend sollution to let the user create a pool of "Special categories" which I eventualy want to use to create a query containing every "portfolio item" that has at least one of these categories.

So for example: I have the following portfolio items with the following categories:

1. "Item1" - "photography","concepting","clientA"
2. "Item2" - "concepting","clientB"
3. "Item3" - "branding","clientC"

The sollution I want to create for the backend should let the user create an array of categories, where they can choose from every category that is linked to a portfolio item.

So If the user added: "clientA" and "clientB" to this sollution, then I want my query to return "Item1" & "Item2".

How would I go about creating a tool for the user that lets them fill an array of categories, that I can later use to define a query?

I think I need to create a custom menu page that lists all categories linked to a post and then via checkmarks create the array of categories. But I'm not sure how to create and store this array.

My actual plugin based on Pabamato's answer:

add_action( 'admin_menu', 'show_specific_cats' );    

function show_specific_cats() {
    add_menu_page('Kies de categories', 'Manage categories', 'manage_options', 'show-spec-cats', 'category_options');
}

function category_options() {
    if ( !current_user_can( 'manage_options' ) )  {
        wp_die( __( 'You do not have sufficient permissions to access this page.' ) );
    }

    $categories = get_terms( 'category', 'orderby=count&hide_empty=0' );

    if($_POST) {
        $theCats = [];
        foreach($_POST  as $key => $value) {
            array_push($theCats , $value);
        }
        update_option( 'show_these_cats', $_POST );
    }

    $showTheseCats = get_option('show_these_cats');

    echo '<form method="post">';
        echo '<input type="hidden" name="empty" value="0" />';
        echo '<ul>';
        foreach($categories as $key => $value){
            echo '<li>'.
                '<input type="checkbox" name="checkbox[]"';
            if($showTheseCats['checkbox']){
                if(in_array($value->term_id, $showTheseCats['checkbox'])) {
                    echo 'checked';
                }
            }
            echo
                ' value="'.
                $value->term_id.
                '">'.
                $value->name.
            '</li>';
        }
        echo '</ul>';
        echo '<input type="submit" value="Opslaan">';
    echo '</form>';
}

The array of categories can be called via the custom option show_these_cats.

My query on page is now like this:

    $showTheseCats = get_option('show_these_cats');
    if($showTheseCats[checkbox]){
        $args = 'cat='. implode(', ', $showTheseCats[checkbox]).'';
        query_posts( $args );

        while ( have_posts() ) : the_post();
            echo '<li>';
            the_title();
            echo '</li>';
        endwhile;
        wp_reset_query();
    }

Answer 1

You can use

https://codex.wordpress.org/Function_Reference/get_terms

to return the needed data for the select, and store the selected values (term IDs) in options table using

https://codex.wordpress.org/Function_Reference/update_option

The 'hide_empty' param in 'get_terms' will prevent returning categories with no posts.