Crowded is when there are a lot of people or objects. Full when something can hold people/ojects/whatever and it is holding as much as it can. A glass of water can be full, but it cannot be crowded. A subway can be crowded when it is full of people. The sentence doesn't sound correct from your book.

Does your workbook say full/crowded? As in - you need to choose one? As it is written, it does not make sense.