Answer: It is possible to obtain 2 quarts in either the 7 quarts pitcher or the 4 quarts pitcher.
Explanation: Begin by pouring the liquid of the 10 quarts pitcher into the 7 quarts pitcher until it is full, this would leave the 10 quarts pitcher with only three quarts of liquid. Continue by pouring the liquid from the 7 quarts pitcher into the 4 quarts pitcher until full, this would result in the 7 quarts pitcher with only 3 quarts of liquid. Pour the remaining three quarts of liquid of the 10 quarts pitcher into the 7 quarts pitcher, this would render the 10 quarts pitcher empty, and the 7 quarts pitcher with 6 quarts of liquid. Then, continue by pouring the full content of the 4 quarts pitcher into the 10 quarts pitcher, rendering the 4 quarts pitcher empty and the 10 quarts pitcher with 4 quarts of liquid. Finally, pour the liquid from the 7 quarts pitcher into the 4 quarts pitcher until it is full, resulting in the 7 quarts pitcher with only two quarts of liquid, the 10 quarts pitcher with four quarts of liquid and the 4 quarts pitcher completely full.
If you would like to get the 4 quarts pitcher with only 2 quarts of liquid, continue the process by emptying the contents of the 4 quarts pitcher into the 10 quarts pitcher, which would now hold eight quarts of liquid. Then, pour all the contents of the 7 quarts pitcher into the 4 quarts pitcher, resulting in said pitcher having 2 quarts of liquid, rendering the 7 quarts pitcher empty.