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Parentheses are used in mathematics to group numbers or terms, and they signal that the operations within them need to be performed first. In an expression like \((8-6) \cdot (4-7)\), the parentheses indicate which subtraction operations should be completed before moving on to multiplication.

Using parentheses helps to clarify and eliminate any ambiguity in mathematical expressions. When you see parentheses, always remember to perform these calculations before addressing any other operations outside the brackets.

This initial step is crucial to ensure you simplify complex expressions correctly. So, in this exercise, solving each subtraction inside the parentheses is the first priority.

Subtraction involves taking away one quantity from another. It is one of the basic operations in arithmetic and is denoted by the minus sign \(-\). In the exercise \((8-6) \cdot (4-7)\), subtraction is performed inside the parentheses, following the order of operations rules.

It's important to solve each subtraction separately before handling any other operations. Calculate \(8 - 6\) to get \(2\), and \(4 - 7\) to yield \(-3\). Each result you obtain from these operations will be used in the multiplication step.

The process of careful subtraction first is key as it sets up the correct values for multiplication. Ensuring your subtraction is accurate will greatly help your success in solving these types of arithmetic expressions.

Once subtraction within all parenthetical groups is completed, multiplication is typically the next step. In \[2 \cdot (-3)\] from the earlier solved subtraction problems of \((8-6)\) and \((4-7)\), you multiply the resulting numbers.

The multiplication here involves multiplying a positive number with a negative number. Remember the simple rule: a positive times a negative gives a negative result. Hence, multiplying 2 by \(-3\) results in \(-6\).

This is the final step for this particular expression, demonstrating why keeping operations orderly and adhering to their proper sequence is essential in math.