Given that $y$ is directly proportional to $x$, we can express this relationship as:

$y = kx$

where $k$ is the constant of proportionality.

Step 1: Find the constant $k$

Using the values $x = 512$ and $y = 128$:

$128 = k \times 512$

Solve for $k$:

$k = \frac{128}{512} = \frac{1}{4}$

Step 2: Use the constant to find $y$ when $x = 64$

Now that we know $k = \frac{1}{4}$, substitute $x = 64$ into the equation $y = kx$:

$y = \frac{1}{4} \times 64 = 16$

Thus, the value of $y$ when $x = 64$ is 16.

The correct answer is C. 16.

Would you like further clarification or more details on this?

Here are 5 related questions to expand this topic:

1. What happens to $y$ if $x$ is halved in a direct proportion?
2. How do you solve problems involving inverse proportionality?
3. Can a direct proportionality equation include additional constants?
4. What are some real-life applications of direct proportionality?
5. How does direct proportionality differ from linear functions?

Tip: In direct proportionality, as one variable increases, the other increases at the same rate, keeping the ratio between them constant.