Two events are independent of each other, this is called Compound Probability. Classical example is if two coins are filped, what is the probability of getting two heads in a row.?

Answer: each has 50% probability because there are two states only, either H or T. since we have two coins the probability of getting two heads in row is the product of obtaining heads for each individual coin (which is independent of each other). or is $\frac{1}{2}$ × $\frac{1}{2}$ = $\frac{1}{4}$ = 25%. (Notice!).

Back to our problem, now here we have 3 paint brands and one of them is the right paint brand and two of them are not correct brands. so the prabablity that the customer has picked not correct brand is $\frac{2}{3}$ and her husband has not picked correct brand is also $\frac{2}{3}$ , since two probabilities are compound probabilities i.e indepandant of each other the probablity that both woman and her husband fail get correct brand is the product of the two and is = $\frac{2}{3}$ × $\frac{2}{3}$ = $\frac{4}{9}$ .