(3i)(-2+4i) -6+12i -12-6i -2+7i 12+6i

To solve the expression \((3i)(-2+4i)\), we need to distribute \(3i\) to both terms inside the parentheses.<br /><br />First, distribute \(3i\) to \(-2\):<br />\[ 3i \cdot (-2) = -6i \]<br /><br />Next, distribute \(3i\) to \(4i\):<br />\[ 3i \cdot 4i = 12i^2 \]<br /><br />Since \(i^2 = -1\), we have:<br />\[ 12i^2 = 12(-1) = -12 \]<br /><br />Now, combine the results:<br />\[ -6i + (-12) = -12 - 6i \]<br /><br />So, the correct answer is:<br />\[ -12 - 6i \]<br /><br />Therefore, the correct choice is:<br />\[ -12 - 6i \]