The page that you have sent me does not have the set session value behavior applied.
The only set of instructions we have for creating Double Opt In is in this thread, we do not have a tutorial with pictures available.
You have not yet followed the steps from my previous reply:
Make sure you have cookies toolkit installed.
Then go to the server behaviors panel, click the plus button and select WA Cookies -> Set Session value.
Set the trigger to Any Form Post. Set the name to "randomConfirm" click the plus button next to value and select the Random Password option from the bindings panel.
In t he insert record behavior, you can set the new randomString column to use the randomConfirm session variable as it's value.