Here is the response I received:
You may select the three consecutive months you prefer, including retroactively counting nights already stayed for the first two months of the three month window.
Eligible nights are only paid nights in an eligible paid stay with Starpoint eligible room revenue which posts to your account. Although this offer assists you with reaching an elite level, SPG Award nights do not count toward this offer, as this offer is a promotion.
Once the challenge is met (18 nights within the three month period) it takes three to five days before the Platinum Status upgrade will be applied to your account.
You cannot be registered for a Platinum Status Challenge after successfully meeting a prior status challenge.
Through the end of this month, you may select one of the following three consecutive month combinations:
November 1, 2011 to January 31, 2012
December 1, 2011 to February 28, 2012
January 1, 2012 to March 31, 2012.