Quitting can be tough to do, so let's begin with my favorite of the 弃’s.
Qiqi - Back at home Chi Chi's was the 'famous' restaurant that served mexican food so tasty, that it kind of burned down and was replaced by (I can't remember for the life of my right now, but I'll get back to you UPDATE: name is Que Pasa. And my order of the closings is reversed, Que pasa was obviously the first one.), which I believe also later closed. Interestingly, a lot of the properties got sold to Outback and that's how Outback was born. Chain restuarant geneologies are far more interesting than Chinese and I encourage you to explore them. I encourage even myself to start a webpage documenting these things for the public good. Oh, Irving's. Anyway, they didn't burn down, they had the largest hep A outbreak (the chinese one!) in US history (kinda remember that) and then just dissappeared. But you can still buy their salsa (not that great). Sadder, from the wikipedia page, they got rejected when trying to trademark 'salsafication.' I understand the tm office's logic, but still, they needed that. If you have to apply for that kind of word, you should get a pitty approval.
丢弃 = 扔掉, garbage, toss it aside，drop, abandon
放弃 = to give up (something), 习惯， 等等。 主动不要，主动停止。
抛弃- pao1qi4 不喜欢而不要，不喜欢而放弃、扔掉。 Most often translated as abandon.
If they give you a question like this, it'll be clear. You have to know the collocations, that's it.
There's also 舍弃 and a few other important 弃’s which I'm not going to go over now, but you should know as well