Fred and Wilma were divorced in year $1($before $2019).$ Fred is required to pay Wilma $$12,000$ of alimony each year until their child turns $18.$ At that time, the payment will be reduced to $$10,000$ per year. In year $3,$ in accordance with the divorce agreement, Fred paid $$0,000$ directly to Wilma and $$6,000$ directly to the law school Wilma is attending. What amount of the payments received in year $3$ is income to Wilma?

A$.$ $$6,000$

B$.$$$10,000$

C$.$ $$12,000$

D$.$ $$0$