A single die is rolled twice. Find the probability of rolling an even number the first time and a number greater than 4 the second time. Find the probability of rolling an even number the first time and a number greater than 4 the second time. (Type an integer or a simplified fraction.)

Step 1 ：A single die is rolled twice. The die has 6 faces, so the total number of outcomes is \(6*6 = 36\).

Step 2 ：The even numbers on a die are 2, 4, and 6, so there are 3 favorable outcomes for the first roll.

Step 3 ：The numbers greater than 4 on a die are 5 and 6, so there are 2 favorable outcomes for the second roll.

Step 4 ：The two events are independent, so the probability of both events occurring is the product of their individual probabilities.

Step 5 ：The probability calculated seems to be in decimal form. To match the format of the question, it would be better to express this probability as a simplified fraction.

Step 6 ：Final Answer: The probability of rolling an even number the first time and a number greater than 4 the second time is \(\boxed{\frac{1}{216}}\).