Count how many galleries the post has and count all the images. Does require WP 3.6+

gistfile1.php

<?php
// Get all the galleries in the current post
$galleries = get_post_galleries( get_the_ID(), false );
// Count all the galleries
$total_gal = count( $galleries );
/**
 * count all the images
 * @param array $array The array needed
 * @return int returns the number of images in the post
 */
function _get_total_images( $array ){
	$key = 0;
	$src = 0;
	while ( $key < count( $array ) ){
		$src += count( $array[$key]['src'] );
		$key++;
	}
	return intval( $src );
}

echo _get_total_images( $galleries );