Halacha forbids partaking of milk or dairy foods for six hours after one has eaten meat. The question arises as to whether one may sit at a table during this six-hour period with people eating dairy products. Halacha clearly forbids two friends or acquaintances to sit together at a table as one eats meat and the other eats dairy foods, out of concern that they might share each other's food and thus violate the prohibition of eating meat with milk. Does this concern apply as well to a person who does not eat meat at the table, but has eaten meat within the previous six hours? Is he allowed to join his friend who eats dairy foods, and eat foods that are neither meat nor dairy, such as fruit?
The Peri Megadim (Halachic work by Rabbi Yosef Teomim, Poland-Germany, 1727-1792; in Mishbetzot Zahav, Yoreh Dei'a 88:2) held that the prohibition against eating at the same table was enacted only when one acquaintance currently eats dairy products and the other currently eats meat. It does not apply to the situation described above, where one person eats dairy foods and the other had eaten meat beforehand. This is also the ruling of the Chid"a (Rabbi Chayim Yosef David Azulai, Israel, 1724-1806), in his work Shiyurei Beracha.
Similarly, Halacha allows a person to prepare dairy food within six hours of his having partaken of meat, and we are not concerned that he might forgetfully partake of the dairy food he currently prepares. Thus, somebody who ate a meat lunch may prepare a dairy supper, even before six hours have passed. This is the position of Chacham Ovadia Yosef, in his work Yabia Omer (vol. 6, Yoreh Dei'a section, 8:5), and this ruling is mentioned as well by Chacham Yitzchak Yosef in his work Issur Ve'heter, p. 123.
Summary: Although one may not partake of milk or dairy products within six hours of eating meat, he may during this period sit with a friend who drinks milk or dairy foods, and partake of food that is neither dairy nor meat at that table. It is permissible to prepare dairy foods during this six-hour period, as well.