To find the product of the modal and median number, we first need to determine the modal number and the median number.

Modal number: The modal number is the number that appears most frequently in the data set.

Median number: The median number is the middle number when the data set is arranged in ascending order.

Given frequencies:

- 5 with frequency 3

- 8 with frequency 2

- 6 with frequency 4

- 2 with frequency 1

Let's arrange the numbers in ascending order:

\(2, 5, 5, 5, 6, 6, 6, 6, 8, 8\)

Now, we can see that the modal number is 6 since it appears the most times (frequency of 4).

The median number is the middle number. Since there are 10 numbers, the middle two numbers are the 5th and 6th numbers. These are 6 and 6. So, the median number is also 6.

Now, we can calculate the product of the modal and median number:

Product = Modal number × Median number = 6 × 6 = 36