using System;

using System.Linq;

using System.Xml.Linq;

using System.Xml;

public class Program

{

    public static void Main()

    {

                    string xml = @"

<result>

<product>

<auto>

  <report>

    <auto>

      <admin></admin>

      <report>

        <search>

          <subjects>

            <subject>

              <name>

                <first>John</first>

                <last>D</last>

              </name>

            </subject>

          </subjects>

        </search>

      </report>

    </auto>

  </report>

</auto>

<auto>

  <report>

    <auto>

      <admin></admin>

      <report>

        <search>

          <subjects>

            <subject>

              <name>

                <first>Jack</first>

                <last>L</last>

              </name>

            </subject>

          </subjects>

        </search>

      </report>

    </auto>

  </report>

</auto>

</product>

</result>";

            string first = "John";

            string last = "D";

            XDocument xd = XDocument.Parse(xml);

            xd.Root.Element("product").Elements("auto").ToList()

                .ForEach(x=>

                    {

                    var name = x.Descendants("name").First();

                    if (name.Element("first").Value != first

                        && name.Element("last").Value != last)

                        x.Remove();

                    });

            Console.WriteLine(xd);

    }

}