Here's another one of those words where the spelling won't help you at all, and you've been getting it wrong since the day you first saw it, because the first person you heard say it out loud got it wrong too. We still get it wrong sometimes, and we know the way we're supposed to say it not. The trick to this word is knowing where to place the emphasis.
With a lot of words, the emphasis falls on the middle syllable, or the center of the phrasing, but that isn't applicable in all cases, this being one of them. You've probably been reading the word as "a-PLICK-able" as we've gone along, and if you did, welcome to the world of failure. The front of the word takes all the weight and should be spoken like an app on your phone, becoming "APP-lick-able", the same as it would be in application which also shares the same root.