We are given the expression:

$4x^2 - 10xy - 8y^2$

Substitute $x = 3$ and $y = 6$ into the expression:

$4(3)^2 - 10(3)(6) - 8(6)^2$

Let's break this down step by step:

1. $4(3)^2 = 4 \times 9 = 36$
2. $10(3)(6) = 10 \times 18 = 180$
3. $8(6)^2 = 8 \times 36 = 288$

Now substitute these values back into the expression:

$36 - 180 - 288$

Now calculate the final result:

$36 - 180 = -144$ $-144 - 288 = -432$

So, the value of the expression is $-432$.

Would you like more details on any step or have any questions?

Here are 5 related questions to explore:

1. What happens if we switch the signs of the terms?
2. How does changing one variable affect the outcome?
3. What is the general form of quadratic expressions in two variables?
4. How can we factor this expression?
5. How does this expression relate to parabolas or conic sections?

Tip: Always simplify powers and multiplications first when evaluating algebraic expressions!