Final answer:
The product of the complex numbers 3 + 4i and 6i is -24 + 18i.
Step-by-step explanation:
The product of the complex numbers 3 + 4i and 6i can be found by multiplying the real parts and the imaginary parts separately and then adding them together.
Using the distributive property, we have:
(3 + 4i)(6i) = 3(6i) + 4i(6i) = 18i + 24i²
Since i² is equal to -1, we can simplify further:
18i + 24(-1) = 18i - 24 = -24 + 18i
Therefore, the product of the complex numbers 3 + 4i and 6i is -24 + 18i, which corresponds to option b.