Shiritori is a game, you can find it on the side bar under 'games'. You can find an explanation there on how to play it.
are you sure the challenge said to create three shiritori? With out renshuu pro you can only create one. Maybe it said to add three words to shiritori, which is fairly easy to do.
Shiritori is a word game where words alternate with sounds in a word that is built to make other words. Typically you take the last sound of the word and use it for the beginning of the next word. You just keep using that pattern as players alternate.
I think that instead of 'create 3 shiritori', as in creating shiritori rounds, the quest is probably asking you to play 3 words in shiritori instead. Follow the instructions that the other two have left on this post and hopefully you'll be good!