How does "penalized for the wrong answer" work on a multiple choice exam?

It means that you lose marks for any wrong answers, so only answer those for which you are certain that your answer is correct. Typically, if you get an answer correct, you'll get +1 and if you don't answer you'll get 0. However, if you answer and get it wrong, you will get -1, i.e. you get penalized for answering incorrectly.