I see that you've uploaded an image with some mathematical problems on it. Let's go through them one by one to solve them:

1. First Problem:

$\frac{4}{5} \times \frac{2}{3}$

This is a multiplication of fractions: $\frac{4}{5} \times \frac{2}{3} = \frac{4 \times 2}{5 \times 3} = \frac{8}{15}$ So, the correct answer is $\frac{8}{15}$, which you have correctly marked.

2. Second Problem:

$16.8 + (-4)$

This is a simple addition with a negative number: $16.8 + (-4) = 16.8 - 4 = 12.8$ It seems like you might have used an incorrect value of -4.2 in the solution steps, but the correct answer should be $12.8$, not $4.2$. Double-check that step.

3. Third Problem:

$4.9 \times 3.2$

This is straightforward multiplication: $4.9 \times 3.2 = 15.68$ You have the correct answer $15.68$ here.

4. Fourth Problem:

$-\frac{1}{6} + \frac{1}{4}$

We need a common denominator to add these fractions: $\frac{1}{6} = \frac{2}{12}, \quad \frac{1}{4} = \frac{3}{12}$ Now, adding: $-\frac{1}{6} + \frac{1}{4} = -\frac{2}{12} + \frac{3}{12} = \frac{1}{12}$ So, the correct answer should be $\frac{1}{12}$, but the solution shows something different, so it looks like there's an error in the process.

Would you like further explanations for any of these problems? Let me know if you have questions or want to go deeper into any of the solutions!

5 Related Questions:

1. How do you find a common denominator when adding or subtracting fractions?
2. Can you explain why multiplying two fractions is done by multiplying the numerators and denominators?
3. How do you handle adding or subtracting a negative number with decimals?
4. Why is finding the greatest common denominator important when working with fractions?
5. What happens when you divide a negative number by a fraction?

Tip:

When dealing with negative numbers, it's helpful to think of subtraction as adding the opposite value to avoid confusion.