multiplication rule with two random events?

Exercise from

"The probability that a student passes Mathematics is 2/3 and the probability that he passes English is 4/9 . If the probability that he will pass at least one subject is 4/5, what is the probability that he will pass both subjects?
(We assume it is based on probability only.)"

My guess would be to apply the multiplication rule because these are two independent events. So the solution would be 2/3 * 4/9 = 8/27. But, according to the solution provided on the website, my solution is wrong. And while I understand the explanation they provide, I do not understand why my version is incorrect.

Is it because the probability of passing a Math and English exam is unlike the probability of drawing two cards from a deck with replacement? Eg. a deck will always have the same 52 cards, but a Math and EN exam can differ in its content, difficulty, length of time required, etc, so multiplying the probabilities of passing them makes no sense, and is like comparing apples and oranges?

Thank you for your help in advance.
Maybe the events are not independent. Try drawing a Venn diagram with two circles M and E and three areas a, b, and c. Set up a+b=2/3, etc and solve for b.