Let's solve these two problems using the correct order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Problem 1

$\frac{12}{8} - \frac{4}{8} + \left(\frac{10 \cdot \frac{1}{5}}{5}\right) - 8^2$

1. Simplify fractions: $\frac{12}{8} = 1.5, \quad \frac{4}{8} = 0.5$ So the expression becomes: $1.5 - 0.5 + \left(\frac{10 \cdot \frac{1}{5}}{5}\right) - 8^2$

2. Evaluate inside the parentheses: $10 \cdot \frac{1}{5} = 2$ Now substitute back: $\frac{2}{5} = 0.4$ So the expression becomes: $1.5 - 0.5 + 0.4 - 64$

3. Follow the operations left to right: $1.5 - 0.5 = 1$ $1 + 0.4 = 1.4$ $1.4 - 64 = -62.6$

The correct value should be one of the options, which seems to have an error based on the given answer choices. Thus, the correct answer is not among the listed options if the PEMDAS rules are correctly followed.

Problem 2

$2(-3 - 6) + 6 - 5^2$

1. Evaluate inside the parentheses: $-3 - 6 = -9$ So the expression becomes: $2(-9) + 6 - 5^2$

2. Multiply: $2(-9) = -18$ The expression now is: $-18 + 6 - 25$

3. Follow the operations left to right: $-18 + 6 = -12$ $-12 - 25 = -37$

Thus, the correct answer is -37.

Would you like to go over any part in more detail, or do you have any questions?

Here are 5 related questions you might find interesting:

1. How would the solution change if the exponent in Problem 2 was positive?
2. What are the implications of using different orders in PEMDAS for a complex expression?
3. Can you provide an example where the Division and Multiplication order in PEMDAS gives different results?
4. How can you use PEMDAS to simplify an expression with nested parentheses?
5. What happens when an exponent is a fraction in the PEMDAS rule?

Tip: When working with PEMDAS, always take care to perform operations within parentheses first, as this can drastically change the outcome.