WPF - change the selected Item of one combobox to the selected item of another combobox

I have two combo boxes in my .xaml file. I would call the first combobox "main combo box ". The other combobox also contains the same set of values as in the the first main combobox.

When I change the selection in the first combobox, I want the selection of the other combobox to be changed to the same value.

I have done it like in the following.

In my viewmodel, I have the following.

  private <MyClass> _firstComboBoxSelection;
  public <MyClass>  FirstComboboxSelection
  {
         set { _firstComboBoxSelection=value; }
         get { return _firstComboBoxSelection ; }

  }

   private <MyClass> _secondComboBoxSelection;
   public <MyClass>  SecondComboboxSelection
   {
         set { _secondComboBoxSelection=value; }
         get { return _secondComboBoxSelection ; }

    }

The comboboxes are like in the following.

       <ComboBox Name="cmbFirst"
                 SelectionChanged="cmbFirst_SelectionChanged"
                 SelectedItem="{Binding FirstComboboxSelection}"
                 ItemSource="{Binding MyData}"
                 DisplayMemberPath="Name" />

       <ComboBox SelectedItem="{Binding SecondComboboxSelection}"
                 ItemSource="{Binding MyData}"
                 DisplayMemberPath="Name" />

MyData is a ObservableCollection of MyClass. MyClass contains the property Name. In my .xaml.cs file I have the following.

  private void cmbFirst_SelectionChanged(...)
  {

        _secondComboBoxSelection=_firstComboBoxSelection;
  }

But it does not change the second combo box as I want it to. Can someone help me to figure out where I have gone wrong ?