"The fashion of this year is totally different from the one of last year."
Translation:La mode de cette année est complètement différente de celle de l'an dernier.
Why is this cette année in one place, but l'an in the other? How can one tell what gender it is supposed to be?
un an / une année.
it is difficult to really distinguish the two, because there is a rule (duration for années, unit of time with a number for an) but there are exceptions.
you can say "l'an dernier" or "l'année dernière", interchangeably.
you can say "cette année" but not "cet an".
As Sitesurf says, it has to be "cette annee." However, I believe both an and annee are accepted in the second half of the sentence.
Yes, it should be correct too. "entièrement" sounds a bit more formal than "complètement" but you can use both.