If it is possible to form a number with the second, the fifth, and the eighth digits of the number $31549786$, which is a perfect square of a two-digit even number, which of the following will be the second digit of that even number?

Let's extract the specified digits from the number $31549786$:
* $2^{\text{nd}}$ digit $=1$
* $5^{\text{th}}$ digit $=9$
* $8^{\text{th}}$ digit $=6$

The available digits are $1,9,6$. We need to form a 3-digit number using these digits that is a perfect square of a two-digit even number.
Possible combinations are $196,169,961,916,619,691$.

* $196=14^2$ ($14$ is an even number)
* $169=13^2$ ($13$ is an odd number)
* $961=31^2$ ($31$ is an odd number)

The unique number satisfying the condition is $196$, which is the square of the two-digit even number $14$.
The second digit of this even number ($14$) is $4$.