Austria-hungary opposed the formation of a “greater serbia” because

Austria-Hungary opposed the formation of a “greater Serbia” because it would post a great threat to Austria-Hungary.

By the time there was a clash on interest towads colonies,and Austria-Haungary opposed Serbia to get any new colonies lest it become stronger and she would have more Bargaining power,which might defeat Austria-Hungary in getting colonies.

Greater Serbia involves Serbia annexing nations with Serbs such as Bosnia, Herzigovina and Croatian. These were land the Austria-Hungary empire desire to had as well therefore opposing the movement.

Hope it helps!

Morning. sorry sjznzbz