The probability of success of rolling an even number in 1 roll = 3/6 = 0.5. This is a constant and Probability of failure = 0.5. There are 2 possible outcomes so it is a Binomial Distribution.
A six sided die has three even numbers, and each roll is independent, so P(success) is constant at 3/6 = 0.5. Since it's constant, the variable X does indeed have a binomial distribution.
So the answer is the second one, which you have selected.