The question is asking to find the value of the expression:

$\frac{x \cdot y^3}{x^3 \cdot y}$

given that $x = -1$ and $y = 2$.

Let's simplify the expression step-by-step:

$\frac{x \cdot y^3}{x^3 \cdot y} = \frac{(-1) \cdot (2^3)}{(-1)^3 \cdot (2)} = \frac{-1 \cdot 8}{-1 \cdot 2} = \frac{-8}{-2} = 4$

So, the value of the expression is 4, which corresponds to option D.

Would you like more details on the simplification process, or do you have any questions? Here are some related questions for further practice:

1. What happens if $x = 1$ and $y = 3$?
2. How would the expression change if the powers of $x$ and $y$ were different?
3. How would the result differ if $x = 0$?
4. Can you rewrite the given expression using only positive exponents?
5. What are the implications of the signs in the expression?

Tip: When simplifying expressions involving exponents, always check if terms can be canceled out or simplified before substituting values!