For the first die, the probability that the number is less than 3 is 2/6 or 1/3 because there are only 2 numbers (1 and 2) which are less than 3. For the second die, the probability that the number is greater than 4 is also 1/3 for only the numbers 5 and 6 satisfy the condition. To obtain the total probability, multiply the two probabilities because of the conjunction "and".
Thus, the answer is 1/9.