How did the assassination of archduke of ausrtria-hungary lead the war between russia and germany

Well, if you wish to be technical, the assignation of the archduke was not the only thing that lead to the war between Russia and Germany, otherwise known as the WW1 (World War One.) The murder of the archduke and his wife was the critical blow that caused the war, but, the tension was heavy between the two countries for years. It was mostly because of nationalism, and imperialism. Nationalism is that strong feeling that your country is the best at everything. Imperialism is when a country tries to conquer as much land as possible. Also, militarism or the glorification of military strength played a strong role in the start of World War One. So, to answer your question, the assignation of the archduke and his wife was simply the excuse both countries needed to start a fight.