This question was asked on the Australian show, "The 1% club." The contestant had to answer in 30 seconds to win $100,000 and he did! Here's the clip .

Now, here's the solution.

The first digit signifies the number of letters in the month's name, the second digit signifies the month's position in the calendar and the rest of the digits signify the product of the first two digits.

For example, in June = 4624, the first digit is the number of letters in the word, 'June' June is the sixth month of the year, so the second digit is 6. Also, 4*6= 24 so the third and fourth digits are 24.

Therefore, August =6848.