How to display the categories of the post? (custom post type)

get_the_terms returns an Array of WP_Term objects on success, false if there are no terms or the post does not exist, WP_Error on failure.

You can always check if your $terms is an array or is_wp_error.

To check if $terms is an array:

<?php $terms = get_the_terms( $post->ID , 'tvshows_categories' );
if ( is_array( $terms ) && ! is_wp_error( $terms ) ) {
    foreach ($terms as $term) {
        $term_link = get_term_link($term, 'tvshows_categories');
        if (is_wp_error($term_link))
            continue;
        echo '<a href="' . $term_link . '">' . $term->name . '</a>, ';
    }
}
?>

Or if you’re on a single post, you can always check if you’re on your custom post type.

To check if you’re on a custom post type on a single page:

<?php 
if ( is_singular('YOUR_CUSTOM_POST_TYPE') ) {
    $terms = get_the_terms($post->ID, 'tvshows_categories');
    foreach ($terms as $term) {
        $term_link = get_term_link($term, 'tvshows_categories');
        if (is_wp_error($term_link))
            continue;
        echo '<a href="' . $term_link . '">' . $term->name . '</a>, ';
    }
}
?>