using System;

using System.Linq;

using System.Collections.Generic;

public class Program

{

    public static void Main()

    {

        var listings = new[]{

            new Listing { ListingDate = new DateTime(2022, 01, 05), ClosingDate = new DateTime(2022, 04, 05) },

            new Listing { ListingDate = new DateTime(2022, 01, 10), ClosingDate = new DateTime(2022, 04, 10) },

            new Listing { ListingDate = new DateTime(2022, 03, 01), ClosingDate = new DateTime(2022, 07, 01) },

            new Listing { ListingDate = new DateTime(2022, 04, 05), ClosingDate = new DateTime(2023, 03, 07) },

        };

        var listingsByMonth = listings

            .SelectMany(l =>

                    {

                        return l.ListingDate.GetMonths(l.ClosingDate.AddDays(-1)) // assuming closing date is exclusive

                            .Select(dt => new KeyValuePair<DateTime, Listing>(dt, l));

                    })

            .ToLookup(kvp => kvp.Key, kvp => kvp.Value);

        foreach(var g in listingsByMonth)

        {

            Console.WriteLine($"{g.Key:yyyy-MM}: {g.Count()}");

        }

    }

}

​

public class Listing

{

    public DateTime ListingDate { get; set; }

    public DateTime ClosingDate { get; set; }

}

​

public static class Extensions

{

    public static IEnumerable<DateTime> GetMonths(this DateTime startDate, DateTime endDate)

    {

        var monthDiff = (endDate.Month - startDate.Month) + (12 * (endDate.Year - startDate.Year));

        var startMonth = new DateTime(startDate.Year, startDate.Month, 1);

        return Enumerable.Range(0, monthDiff + 1)

            .Select(i => startMonth.AddMonths(i));

    }

}