Given information:
- A six-faced dice is biased and twice as likely to show an even number as an odd number when thrown.

To find:
The probability that the sum of two numbers thrown is even when the biased dice is thrown twice.

Solution:
Let's analyze the possible outcomes when a biased dice is thrown twice. We can represent the numbers on the dice as {1, 2, 3, 4, 5, 6}.

Even numbers:
The biased dice is twice as likely to show an even number. Therefore, the probabilities of getting each even number are {2/9, 4/9, 2/9} (total probabilities add up to 2/3).

Odd numbers:
The biased dice is half as likely to show an odd number. Therefore, the probabilities of getting each odd number are {1/9, 2/9, 1/9} (total probabilities add up to 1/3).

Now, let's consider the possible outcomes when the dice is thrown twice:

Even + Even:
- The probability of getting an even number on the first throw is 2/3.
- The probability of getting an even number on the second throw is also 2/3.
- Therefore, the probability of getting an even sum is (2/3) * (2/3) = 4/9.

Even + Odd:
- The probability of getting an even number on the first throw is 2/3.
- The probability of getting an odd number on the second throw is 1/3.
- Therefore, the probability of getting an even sum is (2/3) * (1/3) = 2/9.

Odd + Even:
- The probability of getting an odd number on the first throw is 1/3.
- The probability of getting an even number on the second throw is 2/3.
- Therefore, the probability of getting an even sum is (1/3) * (2/3) = 2/9.

Odd + Odd:
- The probability of getting an odd number on the first throw is 1/3.
- The probability of getting an odd number on the second throw is also 1/3.
- Therefore, the probability of getting an even sum is (1/3) * (1/3) = 1/9.

Total probability of getting an even sum:
To find the total probability of getting an even sum, we add the probabilities of the three cases where the sum is even:
4/9 + 2/9 + 2/9 = 8/9.

Therefore, the probability that the sum of two numbers thrown with the biased dice is even is 8/9, which is not listed among the given answer options. Hence, there seems to be an error in the options provided.