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When evaluating algebraic expressions, the order of operations is critical to getting the correct answer. It's the sequence we follow to ensure we perform calculations systematically. The order is commonly remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Always start with operations inside parentheses, move on to exponents, then tackle multiplication and division, and finally, complete any addition and subtraction. Let's take our example: starting with the parentheses, we calculate the expression \(2(5-2)\) to get \(6\), before moving on to the next steps.

Parentheses play a crucial role in algebraic expressions as they dictate which operations should be performed first. In our exercise, the parentheses enclose the expression \(5-2\). The subtraction within the parentheses is performed before any other operation, simplifying the expression from \(2(5-2)\) to \(2(3)\) or simply \(6\). Parentheses can also change the meaning of expressions drastically, so it's essential to handle them with care.

Exponents are the 'raised numbers' or 'powers' indicating how many times a number is to be multiplied by itself. In our original expression, \(2^{3}\) refers to multiplying 2 by itself three times. Exponents must be evaluated right after any parenthetical calculations. So, after simplifying the operation inside the parentheses, the next step is to calculate \(2^{3}\), which equals \(8\). Understanding exponents is vital, as tackling them at the wrong stage can result in an incorrect answer.

After simplifying expressions with parentheses and exponents, and completing multiplication or division, the final operations in evaluating an algebraic expression are addition and subtraction. They are performed as the last steps and from left to right, just as you read. In the example, once we've computed \(12 + 6 - 8\), we simply add and subtract in that order, arriving at the final answer of \(10\). These operations might seem simple, but they are the anchor that secures the rest of the calculations in place.