Demarco and Janine Jackson have been married for $20$ years and have four children who qualify as their dependents $($Damarcus$,$ Jasmine, Michael, and Candice$).$ The Jacksons file a joint tax return. The couple received salary income of $$103,500$ and qualified business income of $$11,500$ from an investment in a partnership, and they sold their home this year. They initially purchased the home three years ago for $$207,500$ and they sold it for $$257,500.$ The gain on the sale qualified for the exclusion from the sale of a principal residence. The Jacksons incurred $$16,800$ of itemized deductions, and they had $$4,000$ withheld from their paychecks for federal taxes. They are also allowed to claim a child tax credit for each of their children. However, because Candice was $18$ years of age at year end, the Jacksons may claim a child tax credit for other qualifying dependents for Candice. $($Use the tax rate schedules.$)$

 a$.$ What is the Jacksons' taxable income, and what is their tax liability or $($refund$)?$