To simplify (8-6i)(-4-4i) open the brackets and multiply the terms

(8-6i)(-4-4i)

=> 8*-4 - 8*4i - 6i*(-4) - 6i*(-4i)

=> -32 - 32i + 24i + 24i^2

=> -32 - 8i - 24

=> -56 - 8i

**The required product of is -56 - 8i**

(8-6i)(-4-4i)

8x-4 - 8x4i - 6ix(-4) - 6ix(-4i)

-32 - 32i + 24i + 24i^2

-32 - 8i - 24

-56 - 8i

(8-6i)(-4-4i)

just FOIL

multiply 8 by all the numbers in the 2nd parentheses and then do the same with -6i

-32 - 32i + 24i + 24i^2

remember i^2 = -1

-32 - 32i + 24i + 24(-i)

now simplify by combining like terms:

-32 - 8i - 24

-32 - 24 -8i

-58 - 8i

This problem requires to apply the property of distributivity of multiplication over the addition.

We'll remove the brackets:

(8-6i)(-4-4i) = 8*(-4-4i) - 6i(-4-4i)

We'll remove the brackets from the right side:

(8-6i)(-4-4i) = -32 - 32i + 24i + 24i^2

We'll use the fact that i^2 = -1.

(8-6i)(-4-4i) = -32 - 8i - 24

We'll combine real terms:

**(8-6i)(-4-4i) = -56 - 8i**