Dividends in arrears just means that dividends due to cumulative preferred stockholders were not paid. In the case of cumulative preferred stock, these dividends are still owed, but in the case of noncumulative preferred stock, these dividends owed are forfeited.
The example we provide for you on page F7-6 is only if the preferred stock is "participating". However, this MC question does not make any mention of this, and so once the preferred stockholders are paid their dividends in arrears (dividends not paid in the past and thus still owed) and this year's dividends, then the common stockholders are eligible for the rest (no sharing).
Basically, the $8,000 represents the 'remainder' once the preferred shareholders are paid.
Since we have an available pool of $44,000, we first must use it to pay dividends in arrears ($12,000) and then pay the current year preferred dividend ($24,000). That leaves $8,000 available and paid to the common shareholders.