Cuente con la condición IF en la consulta MySQL

Usa sum() en lugar de count()

Prueba a continuación:

SELECT
    ccc_news . * , 
    SUM(if(ccc_news_comments.id = 'approved', 1, 0)) AS comments
FROM
    ccc_news
    LEFT JOIN
        ccc_news_comments
    ON
        ccc_news_comments.news_id = ccc_news.news_id
WHERE
    `ccc_news`.`category` = 'news_layer2'
    AND `ccc_news`.`status` = 'Active'
GROUP BY
    ccc_news.news_id
ORDER BY
    ccc_news.set_order ASC
LIMIT 20