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The substitution method is an essential first step when solving algebraic expressions. It involves replacing a variable with its known value so you can proceed with computations. In this exercise, we have the expression with the variable \(x\). By substituting \(x = -4\), we transform the initial algebraic form into a numerical one:

- Begin by inserting \(x = -4\) into the expression: \[ 8 \left( \frac{-4}{2} + 5 \right) \]
- This step is crucial because it simplifies the problem by removing the variable, allowing direct arithmetic calculations.

Understanding the substitution method aids in tackling various algebra problems, as it converts expressions from algebraic to arithmetic, setting a clear path for solving.

Once substitution is completed, simplifying the expression is the next key step. Simplification involves performing operations within the expressions to reduce it to its simplest form. Breaking it down step-by-step helps in understanding how each mathematical operation contributes to reaching the final solution.

Let's examine our substituted expression:- Evaluate the division first: \(\frac{-4}{2}\) simplifies to \(-2\).
- Having evaluated the division, our expression now looks like: \[ 8(-2 + 5) \]
- Next, resolve the addition inside the parentheses: adding \(-2\) and \(5\) results in \(3\).

Now, the expression is simplified to: \[ 8 \times 3 \]
Simplifying expressions reduces complexity and prepares the expression for final calculations.

Understanding the order of operations guarantees accuracy in evaluating expressions. The widely accepted convention is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

In this exercise, follow these steps:
- Begin with operations inside the parentheses. - For \(8 \left( \frac{-4}{2} + 5 \right)\), handle the operations inside first: \(\frac{-4}{2} + 5\).
- Proceed with addition within the parentheses. - Resolve it to get \(3\), simplifying it to \(8 \times 3\).
- Finally, perform multiplication: calculate \(8 \times 3\) to obtain \(24\).

Being meticulous with the order of operations ensures all calculations are performed correctly, resulting in a valid and accurate conclusion.