Yes you can. For example if the question asks what the appreciation of the USD is versus the Euro given the old exchange rate of 1.1 EUR/USD and new exchange rate of 1.2 EUR/USD, you calculate it as:
(1.2/1.1) - 1 = 9.09%
If you want to calculate the depreciation of the Euro versus the dollar, just take the inverse:
(1/1.2)/(1/1.1) - 1 = negative 8.33% (8.33% depreciation)
to calculate 1/1.2 or 1/1.1 easily on the calculator just enter 1.2 or 1.1 then hit the [1/X] key
They will almost certainly give you the underlying exchange rate movement as part of the problem. If they don’t then you can insert simple proxy numbers to get the percentage appreciation/depreciation, and then run the formulas above using those proxy numbers. For example if they say currency X appreciated 10 percent versus currency Y, use (1.1/1) - 1 as the proxy numbers. To then calculate the depreciation of currency Y you’d use (1/1.1)/(1/1) -1 = 9.09% depreciation.