The expression provided in the image is:

$4.6 - \left\{ 3.2 - \left( 1.8 - \frac{2.2 - 1.8}{1.8} \right) \right\}$

Let's simplify it step by step:

1. Simplify inside the fraction: $\frac{2.2 - 1.8}{1.8} = \frac{0.4}{1.8} \approx 0.2222$

2. Substitute the fraction back into the equation: $1.8 - 0.2222 \approx 1.5778$

3. Simplify the expression within the second set of brackets: $3.2 - 1.5778 = 1.6222$

4. Now simplify the entire expression: $4.6 - 1.6222 = 2.9778$

Thus, the simplified result is approximately:

$\boxed{2.98}$

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

Here are some related questions for deeper understanding:

1. How do you simplify more complex nested expressions?
2. What are common pitfalls when working with fractions in complex expressions?
3. How can rounding affect the accuracy of results in decimal calculations?
4. Could this expression be written in a different form to make simplification easier?
5. Why is it important to follow the order of operations carefully?

Tip: Always handle fractions and decimals with care, especially when they appear in nested operations. Rounding too early can lead to inaccurate results.