To find the constant of variation $k$ for the direct variation $y = kx$, we can use the values given: $y = 32$ when $x = 4$.

Substituting these values into the equation:

$32 = k \cdot 4$

Solving for $k$:

$k = \frac{32}{4} = 8$

So the constant of variation is A. 8.

Would you like further details or have any questions? Here are some related questions you might consider:

1. How would you express the relationship between $y$ and $x$ using the constant of variation?
2. What would happen to $y$ if $x$ doubled?
3. Can you provide another example of direct variation?
4. How does this concept apply in real-life scenarios?
5. What is the difference between direct variation and inverse variation?

Tip: Always remember that in direct variation, the ratio $\frac{y}{x}$ remains constant.