The "Placate" mission can only be selected for villages that are connected to one of your cities.
Complete the mission and increase the village's Vassal Rate to 100% to make the village a vassal of your city. Additionally, if you battle in a vassal village, your units’ Defense value will increase.
Note that villages connected by roads to cities from other forces may be placated by those forces.
*You may find additional villages to interact with after using the "Investigate" command.