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The Order of Operations is a fundamental concept in mathematics that dictates the sequence in which mathematical operations should be performed. This sequence is crucial because performing operations in the wrong order can lead to incorrect results. The popular acronym PEMDAS can help you remember the order:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

In the equation provided, the operations inside the parentheses should be handled first, according to PEMDAS, which is why \(-8 + 6\) was calculated before multiplication with 2. Always keep this order in mind to ensure you are calculating correctly, especially in more complex algebraic expressions.

Algebraic properties are rules that apply to numbers and operations, helping us simplify and manipulate algebraic expressions. These properties include Commutative, Associative, Identity, and Distributive Properties. In the given exercise, we focused on the Distributive Property, which is essential for understanding algebra.The Distributive Property states that multiplying a number by a sum is the same as multiplying each addend separately and then adding the products. Mathematically, it's expressed as \(a(b+c) = ab + ac\). This property simplifies expressions and is used in equations like \(2(-8+6) = -16 + 12\), where 2 is distributed across the terms \(-8\) and \(6\).Understanding the Distributive Property helps in efficiently solving equations and performing operations on algebraic expressions. Mastering these properties provides a solid foundation for tackling more advanced math topics.

Equation simplification is the process of making an equation easier to work with by combining like terms and performing basic mathematical operations. Simplifying equations helps reveal the structure of an expression, which can make solving problems more straightforward.In the exercised equation \(2(-8+6)=-16+12\), simplification involved the application of the Distributive Property. By distributing 2 over the sum \((-8+6)\), we obtained \(-16 + 12\). This kind of transformation aims to turn complex expressions into more manageable ones and often draws from both algebraic properties and order of operations.By consistently practicing simplification, you increase your fluency in handling equations and improve your problem-solving skills. This foundational skill is indispensable not only in basic algebra but also in advanced math and real-world problem-solving.