To determine which expression is equal to [tex]\(-3i(4 - 2i)\)[/tex], we need to simplify the given expression step by step.
1. Use the distributive property to expand the expression:
[tex]\[
-3i(4 - 2i) = (-3i \cdot 4) + (-3i \cdot -2i)
\][/tex]
2. Multiply each term inside the parentheses:
[tex]\[
-3i \cdot 4 = -12i
\][/tex]
[tex]\[
-3i \cdot -2i = 6i^2
\][/tex]
3. Recall that [tex]\( i^2 = -1 \)[/tex]:
[tex]\[
6i^2 = 6 \cdot (-1) = -6
\][/tex]
4. Combine the real and imaginary parts:
[tex]\[
-12i + (-6) = -12i - 6
\][/tex]
Therefore, the expression [tex]\(-3i(4 - 2i)\)[/tex] simplifies to [tex]\(-12i - 6\)[/tex].
So, the equivalent expression is:
[tex]\[
-12 - 6i
\][/tex]
Thus, the correct option is:
[tex]\[
\boxed{-12 - 6i}
\][/tex]
