Kaden is not great at cooking, but wants to contribute to the freshmen class bake sale. He goes shopping for pre-made cookies. Chocolate chip cookies come in packs of $12$ and oatmeal cookies come in packs of $18$. He buys $3$ packs of chocolate chip cookies and $3$ packs of oatmeal cookies. He wants to put the same amount of cookies on each plate. What is the greatest number of plates he can fill so that he has no leftover cookies?