To answer this question, we can use the concept of similar triangles.

Let's consider the first situation where the pillar is 8 feet tall and casts a shadow that is 4 feet long.

We can set up a proportion between the height of the pillar and the length of its shadow:

$\frac{8}{4} = \frac{16}{x}$

Simplifying this proportion, we have:

$\frac{2}{1} = \frac{16}{x}$

Cross-multiplying, we get:

$2x = 16$

Dividing both sides by 2, we find:

$x = 8$

Therefore, when the pillar is 16 feet tall, the length of its shadow would be 8 feet.

So, the correct answer is A) 8.

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