6. As shown in Figure 4, there are five playing cards with point values of $2,3,7,8,9$ respectively. If two cards are drawn at random, the probability that the product of their point values is an even number is $\qquad$ .
2.6. $\frac{7}{10}$.
According to the problem, when the order of drawing cards is not considered, a tree diagram as shown in Figure 12 can be drawn.

From Figure 12, it can be seen that, when drawing two cards from five, there are a total of 10 possible draws, among which, the product of the numbers drawn is even in 7 cases.
Therefore, the probability that the product of the numbers is even is
$$
P=\frac{7}{10} .
$$