After 5,700 years, which is one half-life of carbon-14, the amount of carbon-14 in the sample will be halved. Since the sample originally has 20 grams of carbon-14, after one half-life, it will have:
\[ 20 \text{ grams} \div 2 = 10 \text{ grams} \]
Thus, the correct response is:
10 grams