Answer:
There are 4x3=12 different pairs of goods, but only 6 if the order is unimportant. So in a barter economy with four goods, traders would need to keep track of 6 different price ratios. Specifically, they are: apples:oranges, apples:bananas, apples:grapes, oranges:bananas, oranges:grapes, and bananas:grapes. (If you know that 1 apple trades for 2 bananas, then you automatically know that 1 banana trades for half an apple. That's why you only need to keep track of 6 total exchange ratios in this small economy.)