To simplify $(2 - 4i)(-6 + 4i)$, we can apply the distributive property (also known as the FOIL method for binomials):

$(2 - 4i)(-6 + 4i) = 2(-6) + 2(4i) - 4i(-6) - 4i(4i)$

Now, let's simplify each term:

1. $2(-6) = -12$
2. $2(4i) = 8i$
3. $-4i(-6) = 24i$
4. $-4i(4i) = -16i^2$

Recall that $i^2 = -1$, so:

$-16i^2 = -16(-1) = 16$

Now, let's combine all the terms:

$-12 + 8i + 24i + 16$

Combine like terms:

$(-12 + 16) + (8i + 24i) = 4 + 32i$

Thus, the simplified result is:

$4 + 32i$

Would you like further explanation or details on any step? Here are some related questions you might find interesting:

1. How do you multiply complex numbers using polar form?
2. What is the significance of $i$ in complex numbers?
3. Can we divide complex numbers in the same way as real numbers?
4. How do we find the conjugate of a complex number and why is it useful?
5. What is the geometric interpretation of multiplying complex numbers?

Tip: When working with complex numbers, always remember that $i^2 = -1$, which often simplifies your calculations!