Chapter 11 - Additional Topics - 11.4 - Complex Numbers - Problem Set 11.4 - Page 493: 37

$-6+12i$

We start with the given expression: $2i(6+3i)$ We use the distributive property to multiply: $6(2i)+(2i)(3i)$ We multiply the real and imaginary terms: $12i+6i^2$ Since $i^2$ is equal to $-1$, we simplify the expression as follows: $6(-1)+12i=-6+12i$