How do I link two lists together by observable collection in VB.NET ?

You would use a CollectionViewSource and use grouping. I assume that you are using WPF. Here is a sample: How to: Sort and Group Data Using a View in XAML - WPF .NET Framework | Microsoft Learn[^].

Hereare some more things that you can do with the CollectionViewSource: CollectionViewSource | 2,000 Things You Should Know About WPF[^]

Here is an example using code only: Grouping based on two or more properties[^]

UPDATE

Here is a search with hundreds more examples: wpf CollectionViewSource grouping - Google Search[^]

UPDATE #2

You tend not not try very hard, that is why I pushed you to do your own research and try. That is what being a programmer is all about - learning and solving problems.

Here is what I have used to build a solution to your question: GroupStyle | 2,000 Things You Should Know About WPF[^]. In this code sample, it shows you how to group items in a ListBox control - The Group Name and the Items within that group.

For your requirement, you do not require the Items collection, just the Count. The CollectionViewSource Class[^] has a CollectionViewSource.Source Property[^]. In Xaml, this is the Items collection.

Now for a sample app:
1. Create a new WPF project named: WpfCollectionViewSourceGrouping
2. Add a People class

namespace WpfCollectionViewSourceGrouping;

public class Person
{
    public string Name { get; set; }

    public string Country { get; set; }
}

3. Generate sample data in the MainWindow.cs class:

using System.Collections.ObjectModel;

namespace WpfCollectionViewSourceGrouping;

public partial class MainWindow
{
    public ObservableCollection<Person> People { get; set; } = new();

    private static List<string> countries = new()
    {
        "Australia",
        "Canada",
        "United Kingdom",
        "United States"
    };

    public MainWindow()
    {
        InitializeComponent();

        Random rand = new();
        
        for (int i = 0; i < 20; i++)
        {
            People.Add(new(){ Name = $"Person {i}", Country = countries[rand.Next(0, countries.Count)]});
        }

        DataContext = this;
    }
}

4. Now we can create our window / data views:

<Window x:Class="WpfCollectionViewSourceGrouping.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:scm="clr-namespace:System.ComponentModel;assembly=WindowsBase"
        mc:Ignorable="d"
        Title="MainWindow" Height="450" Width="800">

    <Grid>
        <Grid.Resources>
            <CollectionViewSource x:Key="GroupedView" Source="{Binding People}">
                <CollectionViewSource.SortDescriptions>
                    <scm:SortDescription PropertyName="Country" />
                    <scm:SortDescription PropertyName="Name" />
                </CollectionViewSource.SortDescriptions>
                <CollectionViewSource.GroupDescriptions>
                    <PropertyGroupDescription PropertyName="Country" />
                </CollectionViewSource.GroupDescriptions>
            </CollectionViewSource>
        </Grid.Resources>

        <Grid.ColumnDefinitions>
            <ColumnDefinition />
            <ColumnDefinition />
        </Grid.ColumnDefinitions>

        <ListBox ItemsSource="{Binding People}"
                 HorizontalContentAlignment="Stretch">
            <ListBox.ItemTemplate>
                <DataTemplate>
                    <Grid>
                        <Grid.ColumnDefinitions>
                            <ColumnDefinition />
                            <ColumnDefinition />
                        </Grid.ColumnDefinitions>
                        <TextBlock Text ="{Binding Name}" />
                        <TextBlock Text ="{Binding Country}" Grid.Column="1"/>
                    </Grid>
                </DataTemplate>
            </ListBox.ItemTemplate>
        </ListBox>

        <ListBox ItemsSource="{Binding Source={StaticResource GroupedView}}"
                 HorizontalContentAlignment="Stretch" Grid.Column="1">
            <ListBox.GroupStyle>
                <GroupStyle>
                    <GroupStyle.ContainerStyle>
                        <Style TargetType="{x:Type GroupItem}">
                            <Setter Property="Template">
                                <Setter.Value>
                                    <ControlTemplate>
                                        <Grid>
                                            <Grid.ColumnDefinitions>
                                                <ColumnDefinition />
                                                <ColumnDefinition />
                                            </Grid.ColumnDefinitions>
                                            <TextBlock Text ="{Binding Name}" />
                                            <TextBlock Text ="{Binding Items.Count}" Grid.Column="1"/>
                                        </Grid>
                                    </ControlTemplate>
                                </Setter.Value>
                            </Setter>
                        </Style>
                    </GroupStyle.ContainerStyle>
                </GroupStyle>
            </ListBox.GroupStyle>
        </ListBox>

    </Grid>
</Window>

5. Run the app and you should now see the following: Sample app screenshot[^]

Doing your research using Google Search will yield results. Unless you're on the cutting edge with very new tech, others have encountered similar problems. WPF is over 17 years old, so you are not Robinson Crusoe!

As shown above, you may not find the exact solution that you are looking for however understanding what the code does enables you to find a working solution. This is called programming.

Enjoy!

You don't need an ObservableCollection to "count"; but you can substitute if you want.

public class Org {
   public int Idx;
   public string Etude;
   public string Name;
}

static List<Org> _listOrg = new List<Org>();
static Func<string, int> _countEtudes = ( s ) => _listOrg.Count( x => x.Name.Equals( s ) );

public class HowMany {
   public int Idx;
   public string Name;
   public int HowManyEtudes => _countEtudes( this.Name );
}

(If you don't use statics, you need to "D.I." (dependency inject) the Org list).