Hi  Asifpatel,
Please follow below code.
C#
protected void Button1_Click(object sender, EventArgs e)
{
    string strEmployeeName = string.Empty;
    string bossName = string.Empty;
    foreach (ListItem item in ListBox1.Items)
    {
        strEmployeeName += item.Text + ",";
    }
    foreach (ListItem item in ListBox2.Items)
    {
        bossName += item.Text + ",";
    }
    InsertRecords(strEmployeeName.Remove(strEmployeeName.Length - 1), bossName.Remove(bossName.Length - 1));
}
private void InsertRecords(string employeeName, string bossName)
{
    SqlConnection conn = new SqlConnection(GetConnectionString());
    SqlCommand cmd = new SqlCommand("INSERT INTO EmployeesTest Values(@EmployeeName,@BossName,@EmployeeNumber,@joinedDate,@Address,@city,@postal,@phone)", conn);
    cmd.CommandType = CommandType.Text;
    cmd.Parameters.AddWithValue("@EmployeeName", employeeName);
    cmd.Parameters.AddWithValue("@BossName", bossName);
    cmd.Parameters.AddWithValue("@EmployeeNumber", TextBox1.Text.Trim());
    cmd.Parameters.AddWithValue("@joinedDate", TextBox2.Text.Trim());
    cmd.Parameters.AddWithValue("@Address", TextBox3.Text.Trim());
    cmd.Parameters.AddWithValue("@city", TextBox4.Text.Trim());
    cmd.Parameters.AddWithValue("@postal", TextBox5.Text.Trim());
    cmd.Parameters.AddWithValue("@phone", TextBox7.Text.Trim());
    conn.Open();
    cmd.ExecuteNonQuery();
    conn.Close();
    lblMessage.Text = "Records Successfuly Saved";
}