Which area of europe was a hotbed for nationalist and ethnic tensions that would eventually lead to the start of world war one

The correct answer is the Balkans

There was a lot of multi-ethnic issues and violence in the region as the region only recently managed to get its independence from the Ottomans. This was combined with the pressure from Austria-Hungary who held a part of the region, specifically western Balkans and wanted even more. The war began when Franz Ferdinand got assassinated.

The Balkans.

Explanation:
The Balkans is the region in southeast Europe stretching from Serbia and Bulgaria to the Black Sea.
The Balkans portion of Europe were part of the Ottoman Empire until the early 1900s when they fought for independence.
Serbian nationalism led to the creation of the Black Hand which is the nationalist group responsible for the assassination of Archduke Franz Ferdinand of Austria which is considered the beginning event of World War I.