To increase liabilities in T-accounts, you would:

In accounting, the double-entry bookkeeping system dictates that every transaction affects at least two accounts and requires a balancing of debits and credits. Liabilities represent what a company owes to outside parties, and they are increased by credits. When you credit a liability account, it reflects an increase in obligations, such as loans or payables.

Therefore, to correctly manipulate T-accounts for liabilities, you would apply a credit, which increases the balance of that liability account. This is fundamental in financial accounting, where the balance sheet shows liabilities on the right side, and increasing them occurs through credit entries.

For example, if a company takes out a loan, the liability account for the loan would be credited to reflect that the company now owes more money, thereby increasing its total liabilities. This mechanism ensures that the accounting equation (Assets = Liabilities + Equity) remains balanced and accurately reflects the financial position of the entity.

The other options pertain to different types of transactions or accounting practices. Debiting an account typically decreases liabilities, while entries in cash payments or purchases journals are specific to recording specific types of transactions rather than directly impacting the liability T-accounts in the general sense.