Out of all the Minutemen Radiant quests, this one has the strictest prerequisites. Not only do you have to destroy The Institute, but you also will need to have initiated the evacuation order. This makes sense because the whole point of this quest is to address the sudden population influx that The Institute's destruction caused.
Preston Garvey will randomly assign this mission after you've completed several Minutemen Radiant quests. When you receive his request, travel to the randomly designated settlement. Accept the settlers' requests, then travel once more to the newly marked location.
When you arrive there, kill all nearby hostiles, whether they're Ghouls, Super Mutants or Deathclaws.
Like all other settlements, creating a new one starts with checking in at the workshop. After you've done that, speak with the settler at the previous settlement. Report your success to Preston to complete this quest.