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Simplifying expressions is a fundamental concept in algebra. It often involves reducing an expression to its simplest form without changing its value. In our exercise, we started with the expression \( 4 - (-y - 4) \). The first step to simplify took into account the rules of arithmetic, particularly how to handle negative signs.

When we encounter subtraction of a negative number, it is equivalent to adding its positive counterpart. For instance, turning \(-(-y)\) into \(+y\) and \(-(-4)\) into \(+4\). This process eliminates parentheses and turns the expression into \( 4 + y + 4 \).

Simplifying expressions helps us better understand the relationships between terms, making it easier to solve equations or evaluate them. By removing parentheses and rearranging, we've streamlined a potentially complex expression into one that is much easier to handle.

Like terms are fundamental to simplifying algebraic expressions. Terms that share the same variables and respective exponents in an expression are considered like terms. In the expression we simplified, here are the like terms involved:

- Numerals or constants, like the two 4s in the expression \( 4 + y + 4 \), are alike because they are standalone numbers.

The variable term \( y \) stands alone here as it does not have any like terms in this instance. Understanding how to identify and group like terms is essential when simplifying expressions. It enables the combination and reduction of terms, thereby simplifying the entire process.

Combining constants refers to adding or subtracting numerical values in an expression. These constants are numbers without variables attached to them. In our exercise, once we had the expression \( 4 + y + 4 \), the two constants 4 can be added together.

This step is straightforward – simply add the constants: \( 4 + 4 \). This operation simplifies to 8, resulting in the expression \( y + 8 \).

Combining constants makes your expressions neater and assures only necessary terms are present. It's a small but critical step that significantly simplifies calculations when dealing with algebraic equations.