public class A
{
   public string Name{get;set;}
   public int Number{get;set;}
}

public class B
{
   public A AInstance{get;set;}
}

public List<B> GetBFromA(List<A> aList)
 {
      ...
      List<B> database_bInstances = db.GetBInstances();

      //here I want linq query that will filter to me the B instances from the database, according to the aList
 }

database_bInstances.Where(b => aList.Any(a => (a.Name == b.AInstance.Name)
                                       && (a.Number == b.AInstance.Number)))

List<B> database_bInstances = db.GetBInstances();

 List<B> new_list = database_bInstances
              .Where(b => aList.Contains(b.AInstance));

List<B> database_bInstances = db.GetBInstances();

 List<B> new_list = database_bInstances
              .Where(b => aList.Any(a => b.AInstance.Name == a.Name && b.AInstance.Number == a.Number));

database_bInstances.Where(b => aList.Any(a => (a.Name == b.AInstance.Name)
                                           && (a.Number == b.AInstance.Number)))

database_bInstances.Where(b => aList.Contains(b.AInstance))