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The distributive property is a fundamental algebraic principle that is used widely for simplifying expressions. It allows us to distribute a multiplied value over a set of terms that are added or subtracted within parentheses. Formally, the property tells us that to evaluate something like \(a(b+c)\), we actually perform \(ab+ac\).

When tackling the exercise \(9(y-3)+2y\), the distributive property comes into play in the initial step. Here's how it works in practice: we have \(9\) being multiplied by the terms within the parentheses \(y-3\). Applying the distributive property, we multiply \(9\) by \(y\), and then \(9\) by \(-3\), giving us \(9y-27\). The original expression transforms, accordingly, into \(9y-27+2y\), where the parentheses are no longer needed because we've distributed the multiplication.

In algebra, 'like terms' refer to terms that have the same variables raised to the same power. Essentially, these terms are 'similar' and can be added or subtracted from one another to simplify the algebraic expression. In the provided exercise, after we've distributed the 9 across \(y-3\), we are left with the terms \(9y-27+2y\).

To further simplify this expression, we look for like terms. Here, \(9y\) and \(2y\) are like terms because both contain the variable \(y\) raised to the first power. Thus, we can combine these terms by adding the coefficients (the numbers in front of the variables), which gives us \(9+2\), and consequently \(11y\). This results in a new simplified expression of \(11y-27\), which is the combination of like terms.

Algebraic manipulation encompasses various techniques used to reorder, simplify, and solve algebraic expressions and equations. Distributive property and combining like terms, as showcased above, are core components of algebraic manipulation. As students get comfortable with these individual techniques, they are better equipped to tackle more complex algebraic challenges.

In the context of our example, once we have the simplified expression \(11y-27\), there aren't further manipulations possible to combine terms or factors, as the remaining terms are not like terms. However, algebraic manipulation might involve additional steps in different scenarios such as factoring, canceling, or expanding expressions. Understanding and applying these techniques correctly can cast a light on solutions and shortcuts that would otherwise remain obscure.