Doug Jackson's taxable income is $$46,300.$ How much will he pay in state income tax if the tax rate is $2\%$ on the first $$2,000,3\%$ on the next $$4,000,4\%$ on the next $$4,000,$ and $6\%$ over $$10,000.$

a$.$ $$2,178$

b$.$ $$2,458$

c$.$ $$2,498$

d$.$ $$2,778$