The quest includes three steps that should be fulfilled sequentially. When you start completing the first one - the other two are locked and each of them becomes available upon passing the previous one. As soon as the Mammoth goes on the first expedition, you can proceed with the quest
The quest is special, because once you start it, a 24 hour timer starts ticking away. If you don't complete all stages during this time, the quest will not be completed, and you'll need to start from the beginning.