Let C1 and C2 be the respective cost prices of the first and second share.

Given that 120%(C1)=96, so C1 = 80
Also 80%(C2) = 96 , so C2 = 120.

Hence both the stocks are purchased for 200$ and both of them are sold for 192$. So a loss of 8$

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You can also remember a small note here...

When two articles are sold at the same price and if the gain % (say x%) on one article is same as the loss % (x%)on the other article, then overall there always will be a loss and the overall loos% = (x^2)/100 %.

Coming this problem, since the gain % = loss % = 20%, the overall loss = 4%.

So 96%(C1+C2) = 192.
Hence C1+C2 = 200.

Thus there will be a loss of 8$ in the entire transaction.

Another small note.....

When two articles are purchased at the same price and if the gain % (say x%) from the sale of one article is same as the loss % (x%) incurred from the sale of the other article, then overall there will neither profit nor loss