$.$ In Year $1,$ Corporation E had a net short$-$term capital gain of $$15,000,$ a net long$-$term capital gain of $$8,000,$ and an $$11,000$ short$-$term capital loss carryback from Year $3.$ In Year $1,$ what is Corporation E$$s net long$-$term capital gain after the carryback?

$$ A$.$$$6,000$

$$ B$.$$$0$

$$ C$.$$$8,000$

$$ D$.$$$4,000$