Verified answer

The question you have to answer is about what happens when two cultures are in contact. The scenario usually implies that one culture is dominant and the other is subordinate. So in a Colonial situation the dominant culture would be the incoming one and the subordinate would be the local ones.

In a migration scenario the contrary prevails: the incoming cultures are subordinate and the local one is dominant. (though it might be true that your teacher assumes that both are equal)

So trying to understand the interaction, you see that the dominant culture either exterminates the subordinate ones or 'accepts' them in varied degrees. There is no real exchange of knowledge, mores or customs, just tolerance. After some time in contact the interaction becomes more fluid, because the subordinate cultures have learned the rules and the dominant one begins to accept certain degree of noncompliance due to ignorance or resistance. That situation would be adaptation.

The third and last level of interaction would be integration. The foreign cultures have stopped resisting and have integrated themselves to the dominant mores, perhaps keeping some superficial traits like clothes or food.

Most dominant cultures force integration so yes it can be 'fostered'. Having one official language is a way of 'fostering' integration, since you force people to abandon their mother language or at least handle both.