Multiply $ \dfrac{7}{8} $ by $ t^2 $ to get $ \dfrac{ 7t^2 }{ 8 } $.

Step 1: Write $ t^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{7}{8} \cdot t^2 & \xlongequal{\text{Step 1}} \frac{7}{8} \cdot \frac{t^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 7 \cdot t^2 }{ 8 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7t^2 }{ 8 } \end{aligned} $$

Subtract $2$ from $ \dfrac{-7t^2}{8} $ to get $ \dfrac{ \color{purple}{ -7t^2-16 } }{ 8 }$.

Step 1: Write $ 2 $ 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 $\color{blue}{8}$.

$$ \begin{aligned} \frac{-7t^2}{8} -2 & \xlongequal{\text{Step 1}} \frac{-7t^2}{8} - \frac{2}{\color{red}{1}} = \frac{ -7t^2 }{ 8 } - \frac{ 2 \cdot \color{blue}{ 8 }}{ 1 \cdot \color{blue}{ 8 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -7t^2 } }{ 8 } - \frac{ \color{purple}{ 16 } }{ 8 }=\frac{ \color{purple}{ -7t^2-16 } }{ 8 } \end{aligned} $$

Subtract $6t$ from $ \dfrac{-7t^2-16}{8} $ to get $ \dfrac{ \color{purple}{ -7t^2-48t-16 } }{ 8 }$.

Step 1: Write $ 6t $ 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 $\color{blue}{8}$.

$$ \begin{aligned} \frac{-7t^2-16}{8} -6t & \xlongequal{\text{Step 1}} \frac{-7t^2-16}{8} - \frac{6t}{\color{red}{1}} = \frac{ -7t^2-16 }{ 8 } - \frac{ 6t \cdot \color{blue}{ 8 }}{ 1 \cdot \color{blue}{ 8 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -7t^2-16 } }{ 8 } - \frac{ \color{purple}{ 48t } }{ 8 }=\frac{ \color{purple}{ -7t^2-48t-16 } }{ 8 } \end{aligned} $$