There is an option when you log into irctctourism.com. Once you log in, its there at the bottom as booked tickets history. Alternatively, you can take a printout of a mail you'd have got from irctc. Lastly, the printout of the screenshot you have posted here would also do. All they need is the transaction no and ID details to cross check.
BTW, looking at the price, I think its a non AC dorm you've booked.