Bill orders 8 pizzas, each with pepperoni (and possibly other toppings as well), and Howard orders 6 pizzas, each with sausage (and possibly other toppings as well). Without knowing precisely how many pizzas were ordered in total, what is the minimum number of pizzas that could contain pepperoni only?

The minimum number? zero. Consider if Bill had ordered 8 with peperoni with anchovies.