$query_Yazilar = "SELECT
article.MakaleID,
article.MakaleKat,
article.MakaleKatID,
article.MakaleBaslik,
article.MakaleYazi,
article.MakaleTiklanma,
article.MakaleYayinlamaTarihi,
administrator.YoneticiKulAdi,
administrator.YoneticiKulResim,
category.KategoriAdi,

COUNT(comment.YORUM ID olacak) AS Yorumsayisi // Kac Adet Yorum Yazıldıgını Ogrenmek İçin yazdım

FROM
article
INNER JOIN category ON category.KategoriID = article.MakaleKat
INNER JOIN administrator ON administrator.YoneticiID = article.YoneticiID
INNER JOIN comment ON article.MakaleID = comment.YaziID GROUP BY article.MakaleKatID

ORDER BY MakaleID DESC";

null değerler varsa left join de deneyebilirsiniz.

$query_Yazilar = "SELECT
article.MakaleID,
article.MakaleKat,
article.MakaleKatID,
article.MakaleBaslik,
article.MakaleYazi,
article.MakaleTiklanma,
article.MakaleYayinlamaTarihi,
administrator.YoneticiKulAdi,
administrator.YoneticiKulResim,
category.KategoriAdi,
  
COUNT(comment.YaziID) AS Yorumsayisi // Kac Adet Yorum Yazıldıgını Ogrenmek İçin  yazdım
  
FROM
article, administrator, category, comment
WHERE category.KategoriID = article.MakaleKat
AND administrator.YoneticiID = article.YoneticiID
AND article.MakaleID = comment.YaziID // Makale tablomla Yorum Tablomdaki YaziID lerini birleştirdim
 
GROUP BY comment.YaziID
ORDER BY article.MakaleID DESC";