The thing that the group decides to charge Mike with is “finding a new meeting place.” Mike has no other “job.” Group members usually have individual jobs or responsibilities. The group decided to “charge” or “give the responsibility” of finding a new meeting place to Mike.

Answer 1

In this context, "charging" Mike with finding a new meeting place means assigning him the responsibility to handle this task. The group has decided that it is Mike's job to find a new meeting place, and it is his individual responsibility within the group.