Jasper and Crewella Dahvill were married in year $0.$ They filed joint tax returns in years $1$ and $2.$ In year $3,$ their relationship was strained and Jasper insisted on filing a separate tax return. In year $4,$ the couple divorced. Both Jasper and Crewella filed single tax returns in year $4.$ In year $5,$ the IRS audited the couple's joint year $2$ tax return and each spouse's separate year $3$ tax returns. The IRS determined that the year $2$ joint return and Crewella's separate year $3$ tax return understated Crewella's self$-$employment income, causing the joint return year $2$ tax liability to be understated by $$5,700$ and Crewella's year $3$ separate return tax liability to be understated by $$6,450.$ The IRS also assessed penalties and interest on both of these tax returns. Try as it might, the IRS has not been able to locate Crewella, but they have been able to find Jasper.

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a$.$ What is the maximum amount of tax that the IRS can require Jasper to pay for the Dahvills' year $2$ joint return?