WordPress at a glance
function is not described

wp_count_attachments() WP 2.5.0

Count number of attachments for the mime type(s).

If you set the optional mime_type parameter, then an array will still be returned, but will only have the item you are looking for. It does not give you the number of attachments that are children of a post. You can get that by counting the number of children that post has.

  • Global. wpdb. $wpdb WordPress database abstraction object.
Hooks in function
Return

Object. An object containing the attachment counts by mime type.

Usage

wp_count_attachments( $mime_type );
$mime_type(string/array)
Array or comma-separated list of MIME patterns.
Default: ''

Code of wp count attachments: wp-includes/post.php WP 5.2.2

<?php
function wp_count_attachments( $mime_type = '' ) {
	global $wpdb;

	$and   = wp_post_mime_type_where( $mime_type );
	$count = $wpdb->get_results( "SELECT post_mime_type, COUNT( * ) AS num_posts FROM $wpdb->posts WHERE post_type = 'attachment' AND post_status != 'trash' $and GROUP BY post_mime_type", ARRAY_A );

	$counts = array();
	foreach ( (array) $count as $row ) {
		$counts[ $row['post_mime_type'] ] = $row['num_posts'];
	}
	$counts['trash'] = $wpdb->get_var( "SELECT COUNT( * ) FROM $wpdb->posts WHERE post_type = 'attachment' AND post_status = 'trash' $and" );

	/**
	 * Modify returned attachment counts by mime type.
	 *
	 * @since 3.7.0
	 *
	 * @param object $counts    An object containing the attachment counts by
	 *                          mime type.
	 * @param string $mime_type The mime type pattern used to filter the attachments
	 *                          counted.
	 */
	return apply_filters( 'wp_count_attachments', (object) $counts, $mime_type );
}