Jennifer is divorced and files a head of household tax return claiming her children, ages $4,7,$ and $11,$ as dependents. Her adjusted gross income for $2023$ is $$81,200$ and her pre$-$credit tax liability is $$6,995.$ What is Jennifer$$s total child tax credit for $2023?$

a$.$ $$4,500$

b$.$ $$9,000$

c$.$ $$500$

d$.$ $$6,000$

e$.$ $$9,600$