Multiply $s$ by $ \dfrac{t^4}{2} $ to get $ \dfrac{ st^4 }{ 2 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} s \cdot \frac{t^4}{2} & \xlongequal{\text{Step 1}} \frac{s}{\color{red}{1}} \cdot \frac{t^4}{2} \xlongequal{\text{Step 2}} \frac{ s \cdot t^4 }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ st^4 }{ 2 } \end{aligned} $$

Subtract $6s+1$ from $ \dfrac{st^4}{2} $ to get $ \dfrac{ \color{purple}{ st^4-12s-2 } }{ 2 }$.

Step 1: Write $ 6s+1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{2}$.

$$ \begin{aligned} \frac{st^4}{2} -6s+1 & \xlongequal{\text{Step 1}} \frac{st^4}{2} - \frac{6s+1}{\color{red}{1}} = \frac{ st^4 }{ 2 } - \frac{ \left( 6s+1 \right) \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ st^4 } }{ 2 } - \frac{ \color{purple}{ 12s+2 } }{ 2 }=\frac{ \color{purple}{ st^4 - \left( 12s+2 \right) } }{ 2 } = \\[1ex] &=\frac{ \color{purple}{ st^4-12s-2 } }{ 2 } \end{aligned} $$