In a single throw of a die we can get any one of the six numbers 1, 2, ..., 6 marked on its six faces. Therefore, the total number of elementary events associated with the random experiment of throwing a die is 6.
An even number or a multiple of 3 is obtained if we obtain one of the numbers 2, 3, 4, 6 as an outcome.
∴ Favourable number of elementary events = 4.
Hence, required probability = 46=23