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Understanding the order of operations is crucial when solving algebraic expressions. This set of rules, often remembered by the acronym PEMDAS, tells us the sequence in which to solve parts of a mathematical expression. The abbreviation stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

For the given expression \( (10-16) \cdot (20-26) \), we start by performing the operations within the parentheses, handling the integer subtraction first. It is essential to follow this hierarchy to avoid errors and ensure the correctness of the final result. Following the order of operations leads to accurate and consistent results across various mathematical problems.

Subtraction with integers can sometimes be tricky, especially when subtracting a larger number from a smaller one, resulting in a negative number. To effectively manage integer subtraction, it's helpful to consider the number line concept. If we're subtracting a larger number from a smaller one, we move to the left on the number line, entering the negative territory.

For instance, in our problem \(10 - 16 = -6\), we start with 10 and move 16 units to the left, landing on -6. This is the first step of the solution process, and it's crucial to get it right before moving on to multiplication or any further operations.

Multiplying negative numbers may initially seem counterintuitive. A key rule to remember is that the product of two negative numbers is a positive number. This is because a negative number signifies a reversal in direction, so two reversals will point us back in the original, or positive, direction.

Considering our exercise, when we multiply \( -6 \cdot -6 \), we're effectively reversing the negative direction twice, which yields a positive result, 36. This concept is part of the fundamental rules in algebra and holds true for any two negative numbers being multiplied. Understanding this concept will greatly aid in tackling more complex algebraic operations.