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The distributive property is a foundational concept in algebra that allows us to simplify expressions, particularly when dealing with parentheses. It involves multiplying a single number by each term within a set of parentheses, effectively "distributing" the multiplier across the terms.
To understand the distributive property, consider the expression \(-2(x+3)\). Here, we distribute \(-2\) to both \(x\) and \(3\). The steps involve multiplication as follows: \(-2 \times x\) and \(-2 \times 3\).
This operation transforms the expression into \(-2x - 6\). By distributing, we simplify expressions and transform them to a form where we can easily combine like terms later, moving closer to a solution.

Combining like terms is an essential part of simplifying algebraic expressions. It involves merging terms that have identical variable parts. This process helps to further simplify the expression by reducing it to its simplest form.
In the expression \(-2x - 6 + 2x\), we identify that \(-2x\) and \(2x\) are like terms because they both have the variable \(x\) raised to the same power. To combine them, we add their coefficients: \(-2 + 2\), which results in \(0\).
Thus, the expression simplifies to \(0 - 6\) or simply \(-6\). By combining like terms, we're able to make the expression more manageable and solve it efficiently.

The order of operations is a set of rules used to determine the sequence in which calculations should be performed to ensure accurate results. Often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), these rules govern the evaluation of mathematical expressions.
In the given expression \(-2(x+3)+2x\), we start with the distributive property inside the parentheses as the first step. This is consistent with the "P" in PEMDAS for parentheses.
Next, we focus on the multiplication in the distribution \(-2(x)\) and \(-2(3)\), implementing the order with "M" for multiplication. Once we've distributed and simplified, the final step involves combining like terms, a process effectively under the "A" for addition in PEMDAS, as we add coefficients.
Maintaining the order of operations ensures that our simplifications and solutions are both orderly and correct.