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

$y = kx$

where $k$ is the constant of proportionality. First, we need to find $k$ using the given values $x = 512$ and $y = 128$.

$128 = k \times 512$

Solving for $k$:

$k = \frac{128}{512} = \frac{1}{4} = 0.25$

Now, using this constant $k = 0.25$, we can find $y$ when $x = 64$:

$y = 0.25 \times 64 = 16$

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

The correct answer is:

16

Would you like more details or have any questions? Here are five related questions:

1. What happens to $y$ if $x$ is halved in a direct proportional relationship?
2. How would the equation change if $y$ was inversely proportional to $x$?
3. What is the constant of proportionality in the context of this problem?
4. How can you verify the proportionality relationship with different values?
5. How does the graph of a direct proportional relationship look?

Tip: When dealing with direct proportionality, remember that as one variable increases, the other increases at a constant rate defined by the proportionality constant.