6. Person A and Person B play a "Guess the Number" game with a fair die (the six faces of the die are numbered $1,2, \cdots, 6$). A and B each think of a number on the die, denoted as $a$ and $b$ respectively. If $|a-b| \leqslant 1$, it is said that "A and B are in sync". The probability that A and B are in sync is $\qquad$
6. $\frac{4}{9}$