An increase in Japan's demand for US goods would cause the value of dollar to appreciate? Why is that? The official answer is "Japan will buy more U.S. dollars." However, my thought was that isn't it usually the case that US companies get paid of Japanese yen rather than U.S. dollars? And hence Japan will not need to buy more U.S. goods. What is the problem in my thought?
Most of international trade actually occurs using the US Dollars. So if Japan wanted to purchase more US goods, they would pay in Dollars.
Using of the Dollar facilitates trade because it resolves the inconvenient situation of needing an exporting (non-US) country's local currency for purchasing. Actually, if Japan wanted to purchase more Argentinian goods they would likely also pay in Dollars. There are many reasons for this, but an important one is that the USD is a reputable currency that holds its value, and it is thus used as a global currency. Without the Dollar in the transaction, in order to purchase from Argentina, Japan would need to purchase pesos which they may not want to hold, and would have to pay currency exchange fees.