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Evaluating an expression means determining its value by replacing variables with their given numbers. When we've been given an expression like \(|x| - |y|\), evaluation involves a few strategic steps. First, you replace each variable in the expression with the given numerical values. Here, \(x = -2\) and \(y = 0\). This substitution transforms the original expression into a numerical one: \(|-2| - |0|\).

Now, you must handle each part of the expression according to mathematical rules. For instance, the keys to correctly evaluate involve understanding the absolute value and executing the correct operations in sequence. Keeping the focus on substitution prioritizes accuracy while transitioning from symbolic expressions to actual numbers.

Substitution is a powerful method in mathematics where variables are replaced with known values. It simplifies expressions by transforming them into numerical calculations. In our example, substituting means taking the expression \(|x| - |y|\) and replacing \(x\) with \(-2\) and \(y\) with \(0\). Thus, the abstract becomes concrete:

• For \(x = -2\): Substitute to get \(|-2|\).
• For \(y = 0\): Substitute to get \(|0|\).

Implementing substitution is crucial for evaluating expressions, as it lays the groundwork for further calculations. It is a systematic step that ensures each part of the expression is evaluated using the correct corresponding values.

Arithmetic operations are the basic operations of addition, subtraction, multiplication, and division. They form the foundation of mathematical calculations. Once substitution and expression evaluation set the stage, you perform the required arithmetic operation. In this expression, the main arithmetic operation is subtraction.

After finding the absolute values, perform the subtraction:

• Calculate \(|-2|\) as \(2\).
• Calculate \(|0|\) as \(0\).
• Perform subtraction: \(2 - 0 = 2\).

This operation leads to the final answer. Understanding these arithmetic processes is essential, as mishandling them can lead to incorrect outcomes. Hence, arithmetic operations tie together the process of moving from substitution to the final evaluated expression.