Multiply $-12$ by $ \dfrac{1-2j}{1+j} $ to get $ \dfrac{24j-12}{j+1} $.

Step 1: Write $ -12 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} -12 \cdot \frac{1-2j}{1+j} & \xlongequal{\text{Step 1}} \frac{-12}{\color{red}{1}} \cdot \frac{1-2j}{1+j} \xlongequal{\text{Step 2}} \frac{ \left( -12 \right) \cdot \left( 1-2j \right) }{ 1 \cdot \left( 1+j \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -12+24j }{ 1+j } = \frac{24j-12}{j+1} \end{aligned} $$