Not sure what you mean by "cough". I assume you mean the number on the face.
The rolls are independent, so

For the first roll, there are three ways of getting a number less than 4 (1, 2, or 3) with a probability of

.
For the second roll, there are two ways of getting a number greater than 4 (5 or 6) with a probability of

.
So the probability of both events occurring in the prescribed order is

.