SavingPersonEvent.cs

var db = new SQLiteConnection(new SQLitePlatformAndroid(), Constants.DbFilePath);
db.CreateTable<Person>();
db.CreateTable<Event>();
db.CreateTable<PersonEvent>();

var event1 = new Event
{
    Name = "Volleyball",
    Date = new DateTime(2017, 06, 18),
    Place = "Sports hall"
};

var person1 = new Person
{
    Name = "A",
    LastName = "B",
    PhoneNumber = "123456789"
};


db.Insert(person1);
db.Insert(event1);

person1.Events = new List<Event> { event1 };
db.UpdateWithChildren(person1);

var personStored = db.GetWithChildren<Person>(person1.Id);
var eventStored = db.GetWithChildren<Event>(event1.Id);