what is private constructor in vb.net?...and how to create?

As the name implies a private constructor is a constructor having the access level defined as private. This means that (in most of the scenarios) an instance of the class cannot be created outside the class using this constructor. For information about access level definitions, have a look at Access Levels in Visual Basic[^]

A typical scenario is a singleton where you want to have a single instance of a non-static class. This means that once the instance is created all code is using the same instance of the class. An implementation could look like

Public Class Singleton
   Private Shared ReadOnly TheInstance As Singleton = New Singleton()

   Private Sub New()
   End Sub

   Public Shared ReadOnly Property Instance As Singleton
      Get
         Return TheInstance
      End Get
   End Property
End Class

And the usage like

Dim a As Singleton = Singleton.Instance
Dim b As Singleton = Singleton.Instance

Of course there are other scenarios where a private constructor can be used. For example if you want to define a class and force the usage of a parameter (or parameters) during the construction then you can hide the default constructor by making it private. Consider the following class

Public Class ForcedParameterization

   Private Sub New()
   End Sub

   Public Sub New(somevalue As Integer)

   End Sub
End Class

And the usage

Dim c As ForcedParameterization = New ForcedParameterization() 'Causes an error: Overload resolution failed because no accessible 'New' accepts this number of arguments.
Dim d As ForcedParameterization = New ForcedParameterization(5) ' compiles just fine