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The substitution method is a fundamental technique in algebra used to determine whether a particular value is a solution to an equation. In simple terms, it involves replacing the variable in the equation with the given number and then evaluating the results.

For example, to check if \( -2 \) is a solution for the equation \( 3a + 2 = 2 - a \), we substitute \( a \) with \( -2 \) and see if the equation holds true. The substitution results in an equation with numbers only, which allows us to perform arithmetic operations to determine the validity of the original equation. This process neatly detangles complex expressions, making them accessible for evaluation.

Simplifying an equation is key to solving algebraic puzzles effectively. After substituting variables with values, the next step is to perform the operations indicated, such as multiplication, addition, or subtraction. The goal is to break down the equation to its simplest form, where it becomes apparent whether the sides of the equation are equal or not.

In the given exercise, after substituting \( a \) with \( -2 \), we simplify \( 3(-2) + 2 \) on the left and \( 2 - (-2) \) on the right. The arithmetic reveals that the left side equals \( -4 \) and the right side equals \( 4 \) after simplification, making it clear that the equation is not balanced. This step is crucial as it conveys instantly if we are moving in the right direction or if the assumed solution is incorrect.

Once the equation is simplified, the final and most critical step is checking for equality. This step is about verifying whether the left-hand side and the right-hand side of the equation are equivalent after the substitution and simplification have been carried out.

For our problem statement, when we arrive at \( -4 = 4 \) after simplification, it is plain that the two sides are not equal. In mathematics, equality is fundamental, serving as the very definition of what it means for an equation to be 'solved' or a solution to be 'correct'. Therefore, the number \( -2 \) is not a solution to the equation as it does not maintain equality between the two sides of the equation. Knowledge of this solidity in mathematical truth gives students the confidence needed to affirm solutions or recognize inaccuracies.