The given equation is $4x^2 + xy$, where $x = 3$ and $y = -2$. Let's substitute these values into the equation and calculate the result.

$4x^2 + xy = 4(3)^2 + (3)(-2)$

Now, simplifying step-by-step:

$4(3)^2 = 4(9) = 36$ $3(-2) = -6$ $36 + (-6) = 30$

Thus, the value of $4x^2 + xy$ is $30$. The correct option is 30.

Would you like more details or have any questions?

Here are five related questions for practice:

1. What is the value of $4x^2 + xy$ if $x = 4$ and $y = 2$?
2. How do you simplify expressions with variables when given specific values?
3. If $y = 0$, what will the equation $4x^2 + xy$ simplify to?
4. What is the importance of the order of operations in solving expressions?
5. How do negative values affect the terms in polynomial expressions?

Tip: Always substitute carefully and follow the correct order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).