The image shows a series of fractions with missing values, likely requiring the completion of proportions. Let's solve each one.

1. $\frac{6}{4} = \frac{2}{3}$

We can solve for the missing part by cross-multiplying: $6 \times 3 = 4 \times 2$ This gives $18 = 8$, which is not possible. So, the first one may be incorrect or unsolvable with the given numbers.

2. $\frac{5}{3} = \frac{4}{4}$

In this case: $5 \times 4 = 3 \times 4$ This simplifies to $20 = 12$, which is also not possible.

3. $\frac{8}{5} = \frac{9}{2}$

Cross-multiplying: $8 \times 2 = 5 \times 9$ This gives: $16 = 45$ This also leads to an impossible equality, suggesting that this proportion isn't correct either.

4. $\frac{10}{2} = \frac{C}{3}$

Cross-multiplying: $10 \times 3 = 2 \times C$ This gives $30 = 2C$, so $C = 15$.

5. $\frac{4}{2} = \frac{8}{4}$

Cross-multiplying: $4 \times 4 = 2 \times 8$ This simplifies to: $16 = 16$ This equation is correct.

Let me know if you need further details on any of these calculations, or if you'd like clarification on the problematic ones.

Here are 5 related questions to expand your understanding:

1. How can we verify if a proportion is valid?
2. What are the steps for solving missing values in proportions?
3. How does cross-multiplication work in solving ratios?
4. What are some common mistakes when setting up proportion problems?
5. How are proportions applied in real-life situations like scaling recipes?

Tip: Always double-check the given values in proportions before solving, especially when they lead to seemingly impossible results.