Multiply $ \dfrac{1}{8} $ by $ p $ to get $ \dfrac{ p }{ 8 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{8} \cdot p & \xlongequal{\text{Step 1}} \frac{1}{8} \cdot \frac{p}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot p }{ 8 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ p }{ 8 } \end{aligned} $$

Subtract $ \dfrac{3}{4} $ from $ \dfrac{p}{8} $ to get $ \dfrac{ \color{purple}{ p-6 } }{ 8 }$.

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

$$ \begin{aligned} \frac{p}{8} - \frac{3}{4} & = \frac{ p }{ 8 } - \frac{ 3 \cdot \color{blue}{ 2 }}{ 4 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ p } }{ 8 } - \frac{ \color{purple}{ 6 } }{ 8 }=\frac{ \color{purple}{ p-6 } }{ 8 } \end{aligned} $$

Subtract $ \dfrac{5}{12} $ from $ \dfrac{p-6}{8} $ to get $ \dfrac{ \color{purple}{ 3p-28 } }{ 24 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 3 }$ and the second by $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{p-6}{8} - \frac{5}{12} & = \frac{ \left( p-6 \right) \cdot \color{blue}{ 3 }}{ 8 \cdot \color{blue}{ 3 }} - \frac{ 5 \cdot \color{blue}{ 2 }}{ 12 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ 3p-18 } }{ 24 } - \frac{ \color{purple}{ 10 } }{ 24 }=\frac{ \color{purple}{ 3p-28 } }{ 24 } \end{aligned} $$

Add $ \dfrac{3p-28}{24} $ and $ \dfrac{6}{7} $ to get $ \dfrac{ \color{purple}{ 21p-52 } }{ 168 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 7 }$ and the second by $\color{blue}{ 24 }$.

$$ \begin{aligned} \frac{3p-28}{24} + \frac{6}{7} & = \frac{ \left( 3p-28 \right) \cdot \color{blue}{ 7 }}{ 24 \cdot \color{blue}{ 7 }} + \frac{ 6 \cdot \color{blue}{ 24 }}{ 7 \cdot \color{blue}{ 24 }} = \\[1ex] &=\frac{ \color{purple}{ 21p-196 } }{ 168 } + \frac{ \color{purple}{ 144 } }{ 168 }=\frac{ \color{purple}{ 21p-52 } }{ 168 } \end{aligned} $$