在你的代码中，你的第一个if子句是这样的：

if (egg > 0)

这意味着，只要egg是一个非零的正整数，那么您就执行iff***的主体并忽略它后面的所有else语句***。
您需要在egg > 0条件之前检查totaleggs % 12 == 1条件。
你的for循环需要看起来像这样：

for (int i = 0; i < Chickens; i++)
{
    Console.Write("Eggs: ");
    int egg = Convert.ToInt32(Console.ReadLine());
    totaleggs += egg;

    if (totaleggs % 12 == 1)
    {
        Console.WriteLine("You have {0} eggs which equals {1} dozen and {2} egg left over.", totaleggs, totaleggs / 12, totaleggs % 12);
        Console.ReadLine();
    }
    else
    {
        Console.WriteLine("You have {0} eggs which equals {1} dozen and {2} eggs left over.", totaleggs, totaleggs / 12, totaleggs % 12);
        Console.ReadLine();
    }
}

旁注：你不需要写(int)(totaleggs / 12)，因为totaleggs / 12做的是完全相同的事情。
如果我写这篇文章，我会做一些更像这样的事情：

int totaleggs = 0;

int ReadNumber()
{
    while (true)
    {
        string input = Console.ReadLine();
        if (int.TryParse(input, out int result) && result > 0)
        {
            return result;
        }
        Console.WriteLine("Not a valid number. Please try again.");
    }
}

Console.Write("Enter the number of chickens: ");
int chickens = ReadNumber();

for (int i = 0; i < chickens; i++)
{
    Console.Write("Eggs: ");
    int egg = ReadNumber();
    
    totaleggs += egg;

    int dozens = totaleggs / 12;
    int singles = totaleggs % 12;
    
    string singles_text =
        singles == 1
        ? "1 egg"
        : $"{singles} eggs";

    Console.WriteLine($"You have {totaleggs} eggs which equals {dozens} dozen and {singles_text} left over.");
    Console.ReadLine();
}

“* 目前它只写着‘鸡蛋’剩下，我不知道如何改变这一点？？*”
改变这种情况的一种方法是计算所有需要写入的内容，然后只写一次：

int egg = Convert.ToInt32(Console.ReadLine());
// proceed only if the chicken has at least 1 egg
if (egg > 0)
{
    totaleggs += egg;
    int dozens = totaleggs/12;
    int eggsLeft = totaleggs%12;
    // will add an "s" only if more than 1 egg left
    string plural = eggsLeft > 1 ? "s" : "";

    Console.WriteLine("You have {0} eggs which equals {1} dozen and {2} egg{3} left over.", totaleggs, dozens, eggsLeft, plural);
    Console.ReadLine();
}

**注意：**这样，如果您需要更改句子，只需更改一次。

“谁能告诉我，我做错了什么？”
您错误地使用了if/else if，因为您只会在鸡的蛋数少于1个时才检查剩余的蛋数（* 即 * 如果第一个条件-egg > 0-是false）。
让代码正常工作的一种变化较小的方法是将else if部分 * 移到 * 第一个if中，* 即 * 更改以下内容：

if (egg > 0)
{
    totaleggs += egg;
    Console.WriteLine("You have {0} eggs which equals {1} dozen and {2} eggs left over.", totaleggs, (int)(totaleggs / 12), totaleggs % 12);
    Console.ReadLine();
}
else if (totaleggs % 12 ==1)
{
    Console.WriteLine("You have {0} eggs which equals {1} dozen and {2} egg left over.", totaleggs, (int)(totaleggs / 12),  totaleggs % 12);
    Console.ReadLine();
}
else
{
    Console.WriteLine("You have {0} eggs which equals {1} dozen and {2} eggs left over.", totaleggs, (int)(totaleggs / 12), totaleggs % 12);
    Console.ReadLine();
}

为此：

if (egg > 0)
{
    totaleggs += egg;
    if (totaleggs % 12 ==1)
    {
        Console.WriteLine("You have {0} eggs which equals {1} dozen and {2} egg left over.", totaleggs, (int)(totaleggs / 12),  totaleggs % 12);
        Console.ReadLine();
    }
    else
    {
        Console.WriteLine("You have {0} eggs which equals {1} dozen and {2} eggs left over.", totaleggs, (int)(totaleggs / 12), totaleggs % 12);
        Console.ReadLine();
    }
}

或者，如果你仍然想在没有鸡蛋的情况下打印一些东西，只需将else if更改为if（仍然从第一个if删除打印）：

if (egg > 0)
{
    totaleggs += egg;
    //Console.WriteLine("You have {0} eggs which equals {1} dozen and {2} eggs left over.", totaleggs, (int)(totaleggs / 12), totaleggs % 12);
    //Console.ReadLine();
}
/* else */ if (totaleggs % 12 ==1)
{
    Console.WriteLine("You have {0} eggs which equals {1} dozen and {2} egg left over.", totaleggs, (int)(totaleggs / 12),  totaleggs % 12);
    Console.ReadLine();
}
else
{
    Console.WriteLine("You have {0} eggs which equals {1} dozen and {2} eggs left over.", totaleggs, (int)(totaleggs / 12), totaleggs % 12);
    Console.ReadLine();
}

如果你想得到这样的东西（据我所知）。

Enter the number of chickens: 2
Eggs: 13
You have 13 eggs which equals 1 dozen and 1 egg left over.

Eggs: 15
You have 28 eggs which equals 2 dozen and 4 eggs left over.

那么有几个选择。

选项1（最佳方式）：

这是一句俏皮话，如果，可能看起来很难，但当理解。然后会爱他们。
学习链接：https://learn.microsoft.com/en-us/dotnet/csharp/language-reference/operators/conditional-operator
选项2是相同的，但“凌乱”的变种
代码：

Console.WriteLine("You have {0} eggs which equals {1} dozen and {2} {3} left over.", totaleggs, (int)(totaleggs / 12), totaleggs % 12, totaleggs % 12 == 1 ? "egg" : "eggs");

备选案文2：

代码：

string word;

if (totaleggs % 12 == 1)
{
   word = "egg";
}    
else
{
   word = "eggs";
}
                        
Console.WriteLine("You have {0} eggs which equals {1} dozen and {2} {3} left over.", totaleggs, (int)(totaleggs / 12), totaleggs % 12, word);
Console.ReadLine();

你可能希望for循环的内容是这样的：

for (int i = 0; i < Chickens; i++)
{
    Console.Write("Eggs: ");
    int egg = Convert.ToInt32(Console.ReadLine());

    totaleggs += egg;

    int eggs = totaleggs;
    int dozen = totaleggs / 12;
    int leftover = totaleggs % 12;

    string stotaleggs;
    if (eggs == 1)
        stotaleggs = "egg";
    else
        stotaleggs = "eggs";

    string sleftover;
    if (leftover == 1)
        sleftover = "egg";
    else
        sleftover = "eggs";

    Console.WriteLine("You have {0} {3} which equals {1} dozen and {2} {4} left over.", eggs, dozen, leftover, stotaleggs, sleftover);
    Console.ReadLine();
}

这是相当自我解释。
这可能是写在一个更优雅的方式，但你应该得到的想法。