First, you should separate a process of parsing your input from your business logic. So, your first step is to convert your holidays input to a structure you'll be working with. So, let's say you have a List<Holiday> where

public struct Holiday
{
    public readonly int Month;
    public readonly int Day;
    
    public Holiday(int month, int day)
    {
        Month = month;
        Day = day;
    }
}

Now, in your place I'd start with implementation of something that enumerates working days like so:

public static IEnumerable<DateTime> GetWorkingDays(DateTime startDate, List<Holiday> holidays)
{
    var date = startDate;
    
    for (;;date = date.AddDays(1))
    {        
        if (date.DayOfWeek != DayOfWeek.Saturday &&
            date.DayOfWeek != DayOfWeek.Sunday &&
            holidays.All(holiday => holiday.Day != date.Day ||
                                    holiday.Month != date.Month))
        {
            yield return date;
        }
    }
}

Note that this iterator is endless, so you should be cautious enumerating it.

Now, your problem can be solved with just one line

var result = GetWorkingDays(orderDate, holidays).Skip(workingDays).First();

Complete example here: https://dotnetfiddle.net/W3dalr

First, you should separate a process of parsing your input from your business logic. So, your first step is to convert your holidays input to a structure you'll be working with. So, let's say you have a List<Holiday> where

public struct Holiday
{
    public readonly int Month;
    public readonly int Day;
    
    public Holiday(int month, int day)
    {
        Month = month;
        Day = day;
    }
}

Now, in your place I'd start with implementation of something that enumerates working days like so:

static IEnumerable<DateTime> GetWorkingDays(DateTime startDate, List<Holiday> holidays)
{
    var date = startDate;
    
    for (;;date = date.AddDays(1))
    {        
        if (date.DayOfWeek != DayOfWeek.Saturday &&
            date.DayOfWeek != DayOfWeek.Sunday &&
            holidays.All(holiday => holiday.Day != date.Day ||
                                    holiday.Month != date.Month))
        {
            yield return date;
        }
    }
}

Note that this iterator is endless, so you should be cautious enumerating it.

Now, your problem can be solved with just one line

var result = GetWorkingDays(orderDate, holidays).Skip(workingDays).First();

Complete example here: https://dotnetfiddle.net/W3dalr

First, you should separate a process of parsing your input from your business logic. So, your first step is to convert your holidays input to a structure you'll be working with. So, let's say you have a List<Holiday> where

public struct Holiday
{
    public readonly int Month;
    public readonly int Day;
    
    public Holiday(int month, int day)
    {
        Month = month;
        Day = day;
    }
}

Now, in your place I'd start with implementation of something that enumerates working days like so:

public static IEnumerable<DateTime> GetWorkingDays(DateTime startDate, List<Holiday> holidays)
{
    var date = startDate;
    
    while (true)
    {        
        if (date.DayOfWeek != DayOfWeek.Saturday &&
            date.DayOfWeek != DayOfWeek.Sunday &&
            holidays.All(holiday => holiday.Day != date.Day ||
                                    holiday.Month != date.Month))
        {
            yield return date;
        }
        
        date = date.AddDays(1);
    }
}

Note that this iterator is endless, so you should be caution enumerating it.

Now, your problem can be solved with just one line

var result = GetWorkingDays(orderDate, holidays).Skip(workingDays).First();

Complete example here: https://dotnetfiddle.net/W3dalr

First, you should separate a process of parsing your input from your business logic. So, your first step is to convert your holidays input to a structure you'll be working with. So, let's say you have a List<Holiday> where

public struct Holiday
{
    public readonly int Month;
    public readonly int Day;
    
    public Holiday(int month, int day)
    {
        Month = month;
        Day = day;
    }
}

Now, in your place I'd start with implementation of something that enumerates working days like so:

public static IEnumerable<DateTime> GetWorkingDays(DateTime startDate, List<Holiday> holidays)
{
    var date = startDate;
    
    for (;;date = date.AddDays(1))
    {        
        if (date.DayOfWeek != DayOfWeek.Saturday &&
            date.DayOfWeek != DayOfWeek.Sunday &&
            holidays.All(holiday => holiday.Day != date.Day ||
                                    holiday.Month != date.Month))
        {
            yield return date;
        }
    }
}

Note that this iterator is endless, so you should be cautious enumerating it.

Now, your problem can be solved with just one line

var result = GetWorkingDays(orderDate, holidays).Skip(workingDays).First();

Complete example here: https://dotnetfiddle.net/W3dalr