how would I jounalize product warranty costs of $8,800.?

Answer 1

Warranty cost is something you should have made a provision for before this:
Dr Product warranty costs
Cr Provision for warranty costs

If you had done that, your entry now as you incur the $8,800 will be:
Dr Prov. for warranty costs 8,800
Cr Cash or A/cs payable 8,800

However if you haven't made the provision before, you shld:
Dr Warranty costs 8,800
Cr Cash or A/cs payable 8,800

and start thinking about making that provision.