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Arithmetic operations are the basic calculations we perform in math: addition, subtraction, multiplication, and division. These are essential building blocks that allow us to solve complex problems by breaking them down into simpler steps.

In the given exercise, we see subtraction being used within the parentheses. To execute arithmetic operations, you start by solving individual calculations like \(4 - 2\). This is performed by taking away 2 from 4, resulting in 2.

Understanding and practicing these operations help in solving more elaborate mathematical expressions effectively. Becoming proficient with basic arithmetic is crucial to handle advanced mathematical concepts, such as factorials, as shown in this exercise.

The order of operations is a fundamental principle in math that ensures expressions are evaluated consistently. It is commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

In the exercise here, we start with solving anything inside the parentheses first. This ensures that the expression is simplified systematically. After solving \(4 - 2\), we determine what numerical value to use for the factorial. This order ensures clarity and consistency in more complex calculations.

Failing to follow the correct order often leads to mistakes. Therefore, always handling parentheses first allows for an accurate foundation before moving on to more advanced operations, a critical step when dealing with expressions.

Mathematical expressions represent numbers, operations, and sometimes variables, in a form that we can solve or simplify. They are made up of numbers and operators like addition, subtraction, multiplication, division, and sometimes more advanced symbols like factorials.

In the exercise example \((4 - 2)!\), we simplify the expression by first evaluating within the parentheses and then computing the factorial, represented by the '!' sign. A factorial of a number \( n \) is the product of all positive integers less than or equal to \( n \). In this case, \(2!\) means multiplying all numbers from 2 down to 1, which gives us the result of 2.

Understanding how to read and interpret these expressions is fundamental to successfully solving math problems. They allow various operations to be included and calculated in one combined expression.