How did nationalist feelings endanger the austro hungarian empire? who has this quick

The Austro-Hungarian empire was endangered by feelings of nationalism because there were multiple national groups within the empire. So fulfilling nationalist goals would mean a dividing of the empire. The mere fact that the question refers to the empire as "Austro-Hungarian" is already a strong hint of the issue. Prior to 1867, it had been known as simply the Austrian Empire, but a compromise in 1867 meant that a dual monarchy was recognized (an Austrian ruler and a Hungarian ruler). The Hungarians were given self-governing authority over their own internal affairs in their portion of the empire. Other people groups within the empire would seek their own recognition as well -- Czechs, Serbs, Croats, etc. So where nationalism was a uniting factor in regions like the Italian peninsula and the German territories north of Austria, for the Austrian empire, nationalism was a dividing force.

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