Hi @Fei_Li
It is explained in this course video.
In essence - it’s the path of best probabilities. Similar question
The numbers in D matrix are the indexes of t - which previous tag (t_{i-1}) got you the best probability for this tag in this word.
For example, third column (w_3) indicates that the best way to arrive at t_1, for word w_3 is through the t_3 at word w_2.
In other words, probability is maximum for t_1 at word w_3 if previous word (w_2) was a tag t_3.
Cheers