How is a long term liability that is paid deducted from net income for the current year?

Long term liabilities do not get deducted from net income.

Gross Income - Expenses = Net Income

Net Income - Dividends = Retained Earnings.

Paying a Long Term Liability has the following effects on the accounting equation.

Decrease Assets (generally current as they are usually paid in cash)

Decrease Liabilities (it's less you owe)

Owners (stockholders) Equity is unchanged.