The question states that cotton is 'one' which means it is a wedding anniversary, not necessarily the 1st. hence your (and my) confusion.
The lists I've found vary a little, but boil down to:
paper or cotton is 1st. (Depending on local custom I suppose).
cotton is 2nd. usually.
leather is 3rd.
iron/sugar is 6th.
ivory is 14th. So 1 + 3 + 14 - 6 = 12.
The answers supplied are Lace 13th.
Crystal 15th. and Steel 11th.
If the compiler is of the opinion that paper and cotton can be transposed, then the sum could also be 2 + 3 + 14 - 6 = 13, which is what I've circled. Hope this helps.
Do you have any thoughts on which king introduced the bowler hat to the USA?
http://www.theanswerbank.co.uk/Quizzes-and-Puz zles/Question339770.html