"How many vegetables does he cook?"
Translation:Quanta verdura cucina?
They have different meanings, although both are translated as "to cook". Basically "cucinare" is the act of prepare the food and "cuocere" refers to what happens to the food. See this: http://robinonawire.wordpress.com/2012/08/07/cucinare-v-cuocere-words-easily-confused/