Let's break down and solve the expression in the image step by step.

The expression looks like:

$f \left( -4 \frac{3}{5} + 6 : \left( -1.5 + \left( 5 - \frac{1}{5} \cdot 6 \right) \right) \right) : 2 + 3 : \frac{1}{4} \cdot (-0.13)$

Steps:

1. Fractional values:

   • $-4 \frac{3}{5} = -4 - \frac{3}{5} = -4.6$

2. Parentheses:

   • Start with $-1.5 + \left( 5 - \frac{1}{5} \cdot 6 \right)$
   • $\frac{1}{5} \cdot 6 = 1.2$
   • $5 - 1.2 = 3.8$
   • So, $-1.5 + 3.8 = 2.3$

3. Division:

   • $6 : 2.3$ (this is division) = $\frac{6}{2.3} \approx 2.61$

4. First Part Evaluation:

   • Now evaluate the part inside the function $f$: $-4.6 + 2.61 \approx -1.99$

5. Outside the parentheses:

   • Now, continue with the remaining expression: $(-1.99) : 2 + 3 : \frac{1}{4} \cdot (-0.13)$

6. Second part:

   • $3 : \frac{1}{4} = 3 \times 4 = 12$
   • $12 \cdot (-0.13) = -1.56$

7. Final evaluation:

   • Now, the expression becomes: $(-1.99 : 2) + (-1.56)$
   • $-1.99 : 2 = -0.995$
   • So the final result is: $-0.995 + (-1.56) = -2.555$

Thus, the value of the given expression is approximately:

$\boxed{-2.555}$

Would you like to discuss any part of the solution in detail or have any further questions?

Here are some related questions you might find helpful:

1. How do you simplify complex expressions involving fractions and decimals?
2. What is the order of operations (PEMDAS) and how is it applied in solving expressions like this?
3. How do you handle operations with negative numbers and fractions?
4. Can you explain how division and multiplication interact with decimals and fractions?
5. What are some common mistakes to avoid when working with expressions involving multiple operations?

Tip: Always keep track of the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) when simplifying expressions to avoid errors.