World war ii officially began with hostilities between what two nations?

This is not an easy question. The obvious answer is between Germany and Poland. But there are facts below facts.  The key question really is when had Great Britain and France had enough?

Chamberlain did everything in his power to hold the peace. WWI was very costly for everyone. He did not want to go to war quickly. So Austria was a warning. Then Czechoslovakia which was even a bigger warning. Once the land grab  got inside Poland's borders, there were no more warnings. Britain and France were obligated to honor their treaty to defend Poland. 

There are other pieces to the puzzle, but I think you were asked a straight forward question. The answer is in the first line of this answer.