I am learning myself but let me have a go. The word: SHOES is plural so this means NY has to be written with an A as its ending. The use of a double TT comes in when we are dealing with an ETT word. Like: ett nytt apple. I could be absolutely wrong. But this is how I have come to understand it, so far. Let's hope someone with more knowledge will come in and explain it better then I have done. Good luck.
regular adjectives come in a base form which is used for EN words (ny), an ETT form (nytt) and a PLURAL/DEFINITE form (nya)
if you have access to a laptop or desktop PC, use duolingo on there when you start a new section, as there are grammar notes that explain everything in detail
for adjectives for example, there is a whole table with alternative patterns, i.e. adjectives where the -t and -a endings are applied with a bit of a twist