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The distributive property is a simple yet powerful tool in algebra that helps break down and simplify expressions. It allows you to multiply a single term across terms inside parentheses. In our exercise, this property is applied to the left side of the equation. The equation starts as \[2(y-3)\]Using the distributive property, you multiply 2 by each term within the parentheses separately. This gives you \[2 \times y - 2 \times 3\]Which simplifies to \[2y - 6\]Understanding and applying the distributive property is essential as it helps in rearranging expressions so that they can be simplified or solved more easily.
Always remember to distribute to each term inside the parentheses. This foundational concept will appear often in algebra and beyond.

Isolating variables is a critical step in solving equations. It involves manipulating an equation to get the variable of interest alone on one side. This is often done to find the value of the variable.In our example, after using the distributive property, we have the equation:\[2y - 6 = y - 6\]The goal is to get all the terms with the variable, in this case, \(y\), on one side of the equation. We do this by subtracting \(y\) from both sides:\[2y - y - 6 = y - y - 6\]Simplifying, we get:\[y - 6 = -6\]Here, we've successfully moved all variable terms to one side. This set-up makes it easier to solve for the variable in the next step by further simplifying the equation.

Simplifying equations is all about making an equation easier to work with. After isolating the variables, the next task is to simplify what's left. This often involves basic arithmetic operations to find the variable's value.Returning to our equation:\[y - 6 = -6\]To solve for \(y\), we need to isolate it completely. We achieve this by balancing the equation. Add 6 to both sides:\[y - 6 + 6 = -6 + 6\]This simplifies to:\[y = 0\]The process of simplifying made it possible to "see" the value of \(y\). Simplifying equations usually requires performing operations like addition, subtraction, multiplication, or division equally on both sides. This keeps the equation balanced and leads to the correct solution. Once simplified, you can easily determine the value of the variable, which is our goal here.