Question one asked "How many of these neighborhood configurations are there?"
That means "how many entries are there in this list?"
And we can figure that out the same way we figured out
that there were eight entries in the elementary cellular automata.
We can say that there is two possibilities for each of these seven cells
they each can be either black or white and so there is two to the seventh
possible neighborhood coonfigurations which is equal to 128.
So there is 128 entries in this list and c was the correct answer.
Question two asked "How many different cellular automata rule tables are there?"
Well, that asks how many ways can we fill in these update states for the center cells,
and since there is 128 possibilities, and each time there's two possibilities black or white
we get two times two times two 128 times which is two raised to the 128th power,
a ridiculously large number.