Given that you roll a 6-sided die and you count the number of each outcome, you need to remember that when you roll a 6-sided die, the probability of occurrence of each outcome is:
It does not matter how many times you roll the die, the probability will always be the same from one roll to another. This means that each roll is independent because the probability of the first roll does not affect the probability of the second one, due the die will always have the same number of faces.
Therefore, you can conclude that it is a binomial random variable.
Hence, the answer is: Option A.