There are a variety of different ways that this might be done. The simplest way might be to use InStr function in VB.NET to find the 'hours' part of the time and add or subtract from it. But then you would have to know which time zone the program is running in and how many time zones away the three other zones selected by the RadioButton components are. You would have to worry about exceeding 24 hours or displaying a time less than zero. (VB.NET can't accomplish time travel ... yet.) In short, there's more to this than meets the eye. Sorry for giving you such a tough assignment ... but look at how much you learned while you were working on it!!!

Microsoft even admits that this is a tough nut to crack! At the Microsoft sponsored site, gotdotnet, they say:

Even Microsoft has trouble with international relationships!

But, considering the other problems, using the .NET Framework objects to solve the problem is still the "way to go". The key class that supports this in the .NET Framework is the TimeZone class. This class has a method that allows you to convert the time at a local timezone (whatever it is) to UTC time. That takes care of the first RadioButton.

It's not a perfect solution (it doesn't take into account daylight savings time, for example) but a fairly adequate way to adjust UTC time for the other two time zones is to use the AddHours method available for the DateTime datatype. After this, just format the time with the ToShortTimeString method and, as they say in Britain, "Bob's your uncle!"

There are certainly more sophisticated ways to do it (again using the .NET Framework) but this one seemed to me to get nearly all of the job done without being really complicated. Here's the code:

Public Class Form1
    Inherits System.Windows.Forms.Form

#Region " Windows Form Designer generated code "

    Dim theUTCTime As DateTime
    Dim localZone As TimeZone = TimeZone.CurrentTimeZone
    Dim TheZone As Integer = 1
    Const GMTZone As Integer = 1
    Const TOKZone As Integer = 2
    Const ATHZone As Integer = 3

    Private Sub Timer1_Tick( _
        ByVal sender As System.Object, _
        ByVal e As System.EventArgs) _
        Handles Timer1.Tick
        theUTCTime = localZone.ToUniversalTime(TimeString)
        Select Case TheZone
            Case GMTZone
                ' Greenwich Mean Time
                TimeBox.Text = theUTCTime.ToShortTimeString
            Case TOKZone
                ' Tokyo Time
                theUTCTime = theUTCTime.AddHours(9)
            Case ATHZone
                ' Athens Time
                theUTCTime = theUTCTime.AddHours(2)
        End Select
        TimeBox.Text = theUTCTime.ToShortTimeString
    End Sub

    Private Sub GMT_CheckedChanged( _
        ByVal sender As System.Object, _
        ByVal e As System.EventArgs) _
        Handles GMT.CheckedChanged
        ' Greenwich Mean Time
        TheZone = GMTZone
    End Sub

    Private Sub TOK_CheckedChanged( _
        ByVal sender As System.Object, _
        ByVal e As System.EventArgs) _
        Handles TOK.CheckedChanged
        ' Tokyo Time
        TheZone = TOKZone
    End Sub

    Private Sub ATH_CheckedChanged( _
        ByVal sender As System.Object, _
        ByVal e As System.EventArgs) _
        Handles ATH.CheckedChanged
        ' Athens Time
        TheZone = ATHZone
    End Sub
End Class