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Negative numbers are essential in mathematics. They are numbers that are less than zero and are typically written with a minus sign in front. These numbers often represent losses, temperatures below freezing, or any value that stands below a starting point. For instance, -8 means 8 units below zero.

When working with negative numbers, it's important to understand their properties, especially when it comes to arithmetic operations. Always keep in mind that the minus sign changes the direction on the number line. Moving in the opposite direction is the core idea of negative values.

Multiplying numbers, especially negative numbers, can initially seem tricky but becomes straightforward with practice. Here are the basic rules:

• Positive * Positive = Positive
• Negative * Negative = Positive
• Positive * Negative = Negative
• Negative * Positive = Negative

The key point from the given exercise is multiplying two negative numbers: The result will always be positive. This happens because two negative signs cancel each other out. For example, \( -8(-8) = 64 \), as both negative signs negate each other, resulting in a positive product.

Integer arithmetic involves performing mathematical operations using whole numbers (integers), which include positive numbers, negative numbers, and zero.

In addition to basic operations like addition, subtraction, multiplication, and division, understanding the behavior of integers during these operations is crucial. For instance, adding a negative number is the same as subtraction, while subtracting a negative number turns into an addition. Multiplying and dividing follow specific rules, as covered in the multiplication rules, especially concerning the outcome signs (positive or negative).

Integrating these three concepts—negative numbers, multiplication rules, and integer arithmetic—allows you to solve complex problems like the provided example efficiently.