Multiply $4$ by $ \dfrac{a}{4a-4} $ to get $ \dfrac{ 4a }{ 4a-4 } $.

Step 1: Write $ 4 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 4 \cdot \frac{a}{4a-4} & \xlongequal{\text{Step 1}} \frac{4}{\color{red}{1}} \cdot \frac{a}{4a-4} \xlongequal{\text{Step 2}} \frac{ 4 \cdot a }{ 1 \cdot \left( 4a-4 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4a }{ 4a-4 } \end{aligned} $$

Multiply $ \dfrac{4a}{4a-4} $ by $ \dfrac{a-1}{a+1} $ to get $ \dfrac{ 4a }{ 4a+4 } $.

Step 1: Factor numerators and denominators.

Step 2: Cancel common factors.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{4a}{4a-4} \cdot \frac{a-1}{a+1} & \xlongequal{\text{Step 1}} \frac{ 4a }{ 4 \cdot \color{red}{ \left( a-1 \right) } } \cdot \frac{ 1 \cdot \color{red}{ \left( a-1 \right) } }{ a+1 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 4a }{ 4 } \cdot \frac{ 1 }{ a+1 } \xlongequal{\text{Step 3}} \frac{ 4a \cdot 1 }{ 4 \cdot \left( a+1 \right) } \xlongequal{\text{Step 4}} \frac{ 4a }{ 4a+4 } \end{aligned} $$