Yup, T is the last letter of the word Coat and you do need to make it 1 letter longer. Only thing is that the new word needs to end with T if you are using the last letter.
You need to post a word following any of these two alternatives:
It must start with the first letter of the last word and be one character shorter.
It must end with the last letter of the last word and be one character longer.
So if you chose the last letter for coat, which is T, you post a word that ends with last last letter T and is 1 letter longer :