To find the price per quart of soy milk, we first need to convert the total volume from pints to quarts.
There are 2 pints in a quart, so a 4-pint carton is equivalent to:
\[ \text{Quarts} = \frac{4 \text{ pints}}{2 \text{ pints/quart}} = 2 \text{ quarts} \]
Next, we take the total cost of the carton, which is $5.36, and divide it by the number of quarts:
\[ \text{Price per quart} = \frac{5.36 \text{ dollars}}{2 \text{ quarts}} = 2.68 \text{ dollars/quart} \]
Thus, the price per quart of soy milk is
\[ \boxed{2.68} \]