Let's solve each proportion presented in the image:

a) $\frac{6}{7} = \frac{9}{a}$

To find the value of $a$, we can use cross-multiplication: $6 \cdot a = 9 \cdot 7$ $6a = 63$ $a = \frac{63}{6}$ $a = 10.5$

b) $\frac{v}{8} = \frac{7}{6}$

Similarly, we use cross-multiplication to solve for $v$: $v \cdot 6 = 7 \cdot 8$ $6v = 56$ $v = \frac{56}{6}$ $v = 9.\overline{3}$ (or $\frac{28}{3}$ as a fraction)

So, the values are: a) $a = 10.5$ b) $v = 9.\overline{3}$ (or $\frac{28}{3}$)

Would you like more details on any step of this solution or have any other questions?

Here are five related questions you might consider:

1. How can you check if your solution to a proportion is correct?
2. What happens if you flip both ratios in a proportion?
3. Can proportions be solved using a method other than cross-multiplication?
4. What are the practical applications of solving proportions in real life?
5. How would you solve a proportion where both ratios include variables?

Tip: When solving proportions, ensure you cross-multiply correctly and simplify your fractions where possible to get the most accurate answers.