The first thing you should do is make sure your paper adheres to the proper APA style for psychological subjects. There are a number of different places to find this information; one of the best is OWL at Purdue, linked below.
APA style is basic, direct, and does not use flowery language, metaphor or symbolism, or the personal pronoun "I." Every fact should be stated simply enough to understand while still being correct and complete. The discussion section is summed up as follows:
In the rest of this section, you return to your original question and tell the reader what your results have to say about it ("The results indicate that...") and what they do not have to say ("However, the results are inconclusive concerning..." or "do not speak to the question of"). In each case, tell why. (psych.upenn.edu)
To cut your word count down, look at your citations. Are you quoting a lot in the discussion? You don't need to directly quote unless there is a very important point, especially in a paper that short. I'd suggest using only one quote, the one that best covers your thesis, and citing other arguments with title and page number only. The bulk of your research or experiment should be fully detailed in the Introduction, Method, and Results sections, and so shouldn't need too much repetition.
Another thing you can do is reread with an eye for clarity; if you explain the same thing twice, you can eliminate one explanation as long as the other is clear and concise. Consider eliminating extra words; using the last sentence as an example, I could cut 33 words to 13 words: "Reread and cut anything you explain twice, rewriting so one explanation covers everything."
Now, in my personal opinion, longer is better; you have less chance of missing out on something important. However, since your teacher explicitly gave you a word limit, you should try hard to get inside it, or at least not too far over. For a 240-word limit, you should aim for 300 at the absolute highest. If you simply cannot get under a minimum without losing important parts of your argument, then keep them in and turn the paper in long. I can't imagine your teacher will penalize you for being thorough.