LB: I didn’t hear the lecture so what I am writing is “speculation”.
Based on what I wrote above,the 98th day of the year is either on the 8th, 9th or 10th of Teves. On each of these days we have a reason to fast. See Rabbi Hoffman’s article:
It may be that the lecturer was stating that the 98th day of the year is a “tragic” day due to these events.