If 12 men or 18 women can reap a field in 14 days, then working at the same rate, 8 men and 16 women can reap the same field in :

Work done by a man in 1 day = $$\frac{1}{14 \times 12} = \frac{1}{168}$$
Work done by 8 men in 1 day = $$\frac{8}{168} = \frac{1}{21}$$
Work done by a woman in 1 day = $$\frac{1}{14 \times 18} = \frac{1}{252}$$
Work done by 16 women in 1 day = $$\frac{16}{252}$$
Work done by 8 men and 16 women in one day $$ = \frac{1}{21} + \frac{16}{252} $$
$$ = \frac{12}{252} + \frac{16}{252} = \frac{28}{252} = \frac{1}{9}$$
Hence it takes 9 days for them to complete the work.
Hence Option A is the correct answer.