A character can have multiple pronunciations due to historical or dialectal factors. Most of them are predictable depending of the word category or word context; however, there are some variance that just have to be memorized.
多 can be pronounced either in the first tone or the second tone (interchangeable) when it functions as an adverb: 多久、多美. Otherwise, only the first tone is used: 很多、多數.
刻 can be either the first or fourth tone when used as a verb: 雕刻、刻印. But only the fourth tone when used as a noun/adjective: 時刻、深刻.
聽 usually is used in the first tone; the second tone variance occurs probably only in Mahjong game: 聽牌.
玩 is used in the fourth tone only in 古玩, which is not a really frequent word.
There are dictionaries an online resources for these kinds of variance. Try to search 破音字 or 一音多字, you might find some useful information.