Problem:
Two dice are thrown simultaneously. Find the probability of getting a multiple of 2 on one dice and a multiple of 3 on the other dice.

Solution:
To solve this problem, we need to find the number of favorable outcomes and the total number of possible outcomes.

Favorable Outcomes:
Let's first consider the favorable outcomes, where one dice shows a multiple of 2 and the other shows a multiple of 3.

Case 1: The first dice shows a multiple of 2 (2, 4, or 6) and the second dice shows a multiple of 3 (3 or 6).
In this case, the possible outcomes are:
(2, 3), (2, 6), (4, 3), (4, 6), (6, 3), (6, 6)
So, there are a total of 6 possible outcomes in this case.

Case 2: The first dice shows a multiple of 3 (3 or 6) and the second dice shows a multiple of 2 (2, 4, or 6).
In this case, the possible outcomes are:
(3, 2), (3, 4), (3, 6), (6, 2), (6, 4), (6, 6)
Again, there are a total of 6 possible outcomes in this case.

Therefore, the total number of favorable outcomes is 6 + 6 = 12.

Total Possible Outcomes:
When two dice are thrown simultaneously, each dice has 6 possible outcomes (1, 2, 3, 4, 5, or 6).
So, the total number of possible outcomes is 6 * 6 = 36.

Probability:
The probability of an event is given by the ratio of favorable outcomes to the total possible outcomes.

Probability = Favorable Outcomes / Total Possible Outcomes
Probability = 12 / 36
Probability = 1 / 3

However, we need to simplify the answer.

Simplification:
To simplify the probability, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 12.

Probability = (12 ÷ 12) / (36 ÷ 12)
Probability = 1 / 3

Therefore, the probability of getting a multiple of 2 on one dice and a multiple of 3 on the other dice is 1/3.

Answer:
The correct answer is option 'C' (1/3).