Another user on here suggested that my use of queries was incorrect so I'm changing the code. However, the pagination in the first block of code (below) isn't showing up in the HTML while the second one (my original) shows up fine.

This one doesn't work (new code):

                    $paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
                    $loop = new WP_Query( array(
                        'post_type' => 'movies',
                        'paged' => $paged,
                        'posts_per_page' => 6
                    ));
                    
                    if($loop->have_posts()){
                        while ( $loop->have_posts() ) {
                            $loop->the_post();

                            << LOOP GOES HERE >>


                   <?php
                      }
                   }
                   my_paginate_links();
                   wp_reset_postdata();
                   ?>

This one works (my original code):

                    $c=0;
                    $i=1;
                    
                    $temp = $wp_query;
                    $wp_query = null;
                    $wp_query = new WP_Query();
                    $wp_query->query('post_type=movies' . '&paged=' . $paged . '&posts_per_page=6');
                    
                    while ( $wp_query->have_posts() ) : $wp_query->the_post(); $c++;


                 << LOOP GOES HERE >>

                <?php
                    endwhile; 
                    my_paginate_links();
                    $wp_query = null;
                    $wp_query = $temp;
                    wp_reset_query();
                ?>

How can I get pagination to show up in the first block of code?

Update

                <?php
                
                    function movies_posts_per_page( $query ) {
                        // exit out if it's the admin or it isn't the main query
                        if ( is_admin() || ! $query->is_main_query() )
                            return;
                        // so its not admin, and its the main query, is it the movies post archive?
                        if ( is_post_type_archive( 'movies' ) ) {
                            // it is!! Set the posts_per_page to 6
                            $query->set( 'posts_per_page', 6 );
                            return;
                        }
                    }
                    add_action( 'pre_get_posts', 'movies_posts_per_page', 1 );
                
                    if (have_posts()) : while (have_posts()) : the_post();
                    
                    $custom = get_post_custom($post->ID);
                    $movie_info = $custom["movie_info"][0];
                ?>

                   << LOOP GOES HERE >>

                <?php endwhile; ?>

                <?php my_paginate_links(); ?>
                
                <?php endif; ?>