As an inventory associate, you are auditing stock adjustments in a warehouse management system. The system uses signed integers to log bulk changes to inventory. You encounter two automated adjustment calculations that need to be manually simplified: $-9(6)$ and $-9(-6)$. According to the rules for multiplying integers, what are the simplified values of these two expressions, respectively?

In a corporate accounting system, automated entries for debt and credit adjustments are often represented as multiplication expressions. To ensure the ledger balances correctly, match each mathematical expression or general sign rule with its corresponding simplified value or product outcome.

Auditing Billing Adjustments

In a corporate inventory system, reversing 9 instances of a 6-unit deduction is represented by the mathematical expression $-9(-6)$. The simplified value of this expression is 54.

Auditing Automated Stock Adjustments

A financial auditor is reviewing recurring debit adjustments on customer invoices. In the ledger system, a subtraction of 6 dollars is represented by the positive integer 6. Applying this subtraction 9 times is modeled by the multiplication expression ${}-9(6)$. According to the rules for multiplying signed numbers, the simplified integer value of this total adjustment is ____.

As a retail store manager, you are auditing the store's digital ledger. An automated script is processing corrections for inventory discrepancies. Two corrections are represented by the multiplication expressions $-9(6)$ and $-9(-6)$. To verify the automated script's calculations, you must manually simplify these expressions step-by-step. Arrange the following steps in the correct order to first simplify the expression $-9(6)$, then simplify the expression $-9(-6)$.