Well, we can answer this fairly easily,

without having to go through
every single cell,

and look up its 
neighborhood in the table.

We can look at this very last cell here,

and we see that its neighborhood is

white white, and then we wrap around

to get white.

Three whites go to

a white,

so the middle, this cell here,

will be white.

So that eliminates B and C.

It's either A or D.

OK. And then let's look at

this cell here

well, black white black,

we see goes to black.

But in choice A, it's white

in choice D, it's black.

So by elimination, you can

know that the correct answer is D.

And you can go through if you want,

to verify and make sure that it all works.

You can go through each one.

But this indeed is the answer.