How did the death of archduke franz ferdinand instigate (urge on) the collapse of peace in europe? *

It was a trigger that showed that there were two competing powers in Europe: Russia and Austria-Hungary (and their allies). 

Franz Ferdinand was killed by a Serbian separatist and the Austrians wanted to see him punished. On the other hand, Russia supported Serbia is saying that Austrian demands ( to be allowed to search for the culprit inside Serbia) were too much. 

This lead to a direct conflict between the two powers (Austria and Russia) and further lead to the war. 

Due to the fact that Archduke Ferdinand was Austria-Hungarian, Austria-Hungary was very angry with the Serbian Nationalists. Russia moved to help their Balkan allies and Germany aided Austria-Hungary because they had a pact. France had a pact with Russia so Germany hit France through Belgium. Britain was an ally of Belgium, and to a lesser extent, France. So the war starts.
 

Ibelieve that the answer is (a).