To find the price per cup of apple juice, first convert quarts to cups. There are 4 cups in a quart, so a 2-quart carton contains:
\[ 2 \text{ quarts} \times 4 \text{ cups/quart} = 8 \text{ cups} \]
Now, the total cost of the 2-quart carton is $2.08. To find the price per cup, divide the total cost by the number of cups:
\[ \text{Price per cup} = \frac{2.08}{8} \]
Calculating this gives:
\[ \text{Price per cup} = 0.26 \]
So, the price per cup of apple juice is $0.26.