You can't with VB. VB and ASP.Net run on the server side so it has no way of knowing that a client has closed its browser. You can do some things on client side using the window.close() event in javascript.
window.onbeforeunload = WindowIsClosing;
function WindowIsClosing() {
if (window.event.clientX < 0 || window.event.clientY < 0) {
if (!Validate()) {
var msg = 'Test';
event.returnValue = msg;
return msg;
}
}
}