Radio buttons has the way to achieve this result, but you still wanted to do this then, Handle the CheckBox.CheckedChanged event with the same sub for all four checkboxes
Private Sub CheckBox1_CheckedChanged(sender As System.Object, e As System.EventArgs) _
Handles CheckBox1.CheckedChanged, CheckBox2.CheckedChanged, CheckBox3.CheckedChanged, CheckBox4.CheckedChanged
Dim senderCheck As CheckBox = DirectCast(sender, CheckBox)
For Each checkbox In {CheckBox1, CheckBox2, CheckBox3, CheckBox4}
If checkbox IsNot senderCheck Then
checkbox.Enabled = Not senderCheck.Checked
End If
Next
End Sub