Fixed exchange rates question

Question 5 from page 98 of BA1 Lecture Notes.
If a country wants to fix its exchange rate, but there is downward pressure on it, does the country have to spend its reserves to buy its currency or sell its currency and earn reserves?
Answer:
It must sell its reserves in exchange for its currency

Could someone explain this please? The way I thought about it was the following. Please correct me if this is wrong. Thanks.

Downward pressure on a country’s exchange rate will cause the government to push it back up again by raising the currency’s value through reducing its supply. In order to reduce the currency’s supply, the government will sell its reserves (e.g. gold, USD etc) in exchange for its currency. This amount of the currency will then be held/”hoarded” by the government, making it not actually be in circulation in the country so the currency’s supply is effectively reduced and its valued is raised back up again.