Multiply $10$ by $ \dfrac{a}{10a+7} $ to get $ \dfrac{ 10a }{ 10a+7 } $.

Step 1: Write $ 10 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 10 \cdot \frac{a}{10a+7} & \xlongequal{\text{Step 1}} \frac{10}{\color{red}{1}} \cdot \frac{a}{10a+7} \xlongequal{\text{Step 2}} \frac{ 10 \cdot a }{ 1 \cdot \left( 10a+7 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10a }{ 10a+7 } \end{aligned} $$

Subtract $ \dfrac{10a}{10a+7} $ from $ 6a $ to get $ \dfrac{ \color{purple}{ 60a^2+32a } }{ 10a+7 }$.

Step 1: Write $ 6a $ 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 first fraction by $\color{blue}{ 10a+7 }$.

$$ \begin{aligned} 6a- \frac{10a}{10a+7} & \xlongequal{\text{Step 1}} \frac{6a}{\color{red}{1}} - \frac{10a}{10a+7} = \frac{ 6a \cdot \color{blue}{ \left( 10a+7 \right) }}{ 1 \cdot \color{blue}{ \left( 10a+7 \right) }} - \frac{ 10a }{ 10a+7 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 60a^2+42a } }{ 10a+7 } - \frac{ \color{purple}{ 10a } }{ 10a+7 }=\frac{ \color{purple}{ 60a^2+32a } }{ 10a+7 } \end{aligned} $$