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Understanding simplification in mathematics involves reducing complex expressions to their simplest form. This process often eliminates unnecessary terms or factors, making expressions easier to work with.

In the exercise, we begin by applying absolute value simplification. Absolute value essentially measures the distance of a number from zero on the number line, ignoring whether it is negative or positive.

• First, calculate the value inside the absolute value: \(8 - 24 = -16\).
• Apply the absolute value, which turns \(-16\) into \(16\), because absolute value takes only the magnitude of the number: \(|-16| = 16\).

This initial simplification prepares the expression for further operations, specifically multiplication and division, making it easier to handle. Always tackle the absolute value first when simplifying an expression. This step ensures that the rest of the process uses a straightforward non-negative number.

Multiplication in this context involves combining our simplified result from the absolute value operation with another number. It's important to remember how to handle multiplication with negative numbers: multiplying a positive number by a negative results in a negative product.

Here’s the multiplication step in our exercise:

• Take the simplified value from the absolute operation, \(16\).
• Multiply \(16\) by \(-2\).
• This results in \(16 \times -2 = -32\).

If you multiply two numbers and one of them is negative, the result will have a different sign from the positive number. This is why our expression becomes \(-32\). Handling signs correctly is crucial in multiplication to avoid errors in more complex expressions.

Division is the final step in our example, and it follows immediately after multiplication. Just like multiplication, division needs careful attention to the signs of numbers.

When dividing by a negative number, the sign of the quotient changes. Let’s take a closer look at our particular division:

• The result from multiplication is \(-32\).
• Divide \(-32\) by the negative number \(-2\).
• Remember that dividing two negative numbers results in a positive number: \(-32 \div -2 = 16\).

Thus, the division reverses the negative sign from the multiplication step. This final operation completes the simplification, resulting in the straightforward answer of \(16\). In such problems, keep your eye on the sign changes between multiplication and division to maintain accuracy.