Let's solve the two parts of the question:

(a) Find the value of $4x - 6y$ when $x = 3$ and $y = -2$:

Substitute the values of $x$ and $y$ into the expression:

$4(3) - 6(-2) = 12 + 12 = 24$

So, the value of $4x - 6y$ is 24.

(b) Find the value of $2a^2 + 5b^2$ when $a = -6$ and $b = 2$:

Substitute the values of $a$ and $b$ into the expression:

$2(-6)^2 + 5(2)^2 = 2(36) + 5(4) = 72 + 20 = 92$

So, the value of $2a^2 + 5b^2$ is 92.

Would you like more details or have any questions on the steps?

Related Questions:

1. What happens if the signs of $x$ and $y$ change in part (a)?
2. How would you solve part (b) if both $a$ and $b$ were positive?
3. Can you generalize the expression in part (a) for arbitrary values of $x$ and $y$?
4. How does the solution to part (b) change if $a$ or $b$ is zero?
5. What if you had to find the value of $4x + 6y$ instead in part (a)?

Tip:

When squaring negative numbers, the result is always positive, as $(-n)^2 = n^2$.