Accepted answer
int requiredId = ...   
var usersInReqdDept = Users.Where(u => u.Departments
                                        .Any(d => d.DepartmentId == requiredId));

If the Departments list can be null, you will need a null-check in the Where clause.

If you want to search the Departments list instead,

int requiredId = ...   
var usersInReqdDept = Departments.Single(d => d.DepartmentId == requiredId)

Of course, this will throw an exception if such a department doesn't exist.

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