According to US laws, Kendrick, having just turned 20, is not legally allowed to buy alcohol, as the legal drinking age in the United States is 21. However, he is allowed to purchase tobacco products, as the legal age for buying tobacco is 21 or sometimes lower in certain states, but since he has turned 20, he is typically permitted to buy tobacco in many places.
Therefore, the most likely answer to what this means is:
He can buy tobacco products but not alcohol.