This is the 3486th most frequent Russian word.
пустыне
"Пустыне" is not a correct form; the correct word is "пустыня," meaning "desert."
Here, 'пустыне' is used in the prepositional case to signify location ('in the desert').
Я видел большую ящерицу в пустыне.
I saw a large lizard in the desert.
In this sentence, 'пустыне' also takes the prepositional case to describe conditions of life in the desert.
Жизнь в пустыне может быть очень трудной.
Life in the desert can be very hard.
Once again, 'пустыне' is in the prepositional case, indicating that the plants are located there ('in the desert').