Anna's total profit was $6000 + $16000 - $4000 = $14000.
How did Anna earn profit
Anna bought $4000 of company stock. The value of the stock doubled when she sold 75% of it, which means she sold 0.75 * $4000 = $3000 worth of stock when its value doubled.
Since the value of the stock doubled, Anna sold the $3000 worth of stock for 2 * $3000 = $6000.
Anna then sold the remainder of the stock (25% of the original amount) for four times the purchase price. Since she originally bought the stock for $4000, the remainder was worth 0.25 * $4000 = $1000.
Selling this remainder for four times the purchase price means that Anna sold it for 4 * $4000 = $16000.