Found the answer, posting the code below so it may help future generations.
<?php
global $wpdb;
$count_terms = $wpdb->get_var ("SELECT COUNT(*)
FROM wp_2_term_taxonomy, wp_2_posts, wp_2_term_relationships
WHERE wp_2_posts.ID = wp_2_term_relationships.object_id
AND wp_2_term_relationships.term_taxonomy_id = wp_2_term_taxonomy.term_taxonomy_id
AND wp_2_term_taxonomy.term_id = '22'
AND wp_2_posts.post_type="post"
AND wp_2_posts.post_status="publish" ");
$count_terms1 = $wpdb->get_var ("SELECT COUNT(*)
FROM wp_3_term_taxonomy, wp_3_posts, wp_3_term_relationships
WHERE wp_3_posts.ID = wp_3_term_relationships.object_id
AND wp_3_term_relationships.term_taxonomy_id = wp_3_term_taxonomy.term_taxonomy_id
AND wp_3_term_taxonomy.term_id = '16'
AND wp_3_posts.post_type="post"
AND wp_3_posts.post_status="publish" ");
$count_terms2 = $wpdb->get_var ("SELECT COUNT(*)
FROM wp_4_term_taxonomy, wp_4_posts, wp_4_term_relationships
WHERE wp_4_posts.ID = wp_4_term_relationships.object_id
AND wp_4_term_relationships.term_taxonomy_id = wp_4_term_taxonomy.term_taxonomy_id
AND wp_4_term_taxonomy.term_id = '13'
AND wp_4_posts.post_type="post"
AND wp_4_posts.post_status="publish" ");
$sum = $count_terms + $count_terms1 + $count_terms2;
echo "<p>Category A sum: {$sum}</p>";
?>