A fair die is rolled 4 times. what is the probability of obtaining a 4,5,4, and a 4 in that order

A fair die would have 6 sides,

Therefore, 6 different numbers has a probability to appear.

Thus, any number has 1/6 chance to appear.

Since you want a specific sequence to occur,

4 results would be (1/6) ^4

Therefore the probability is 1/54