figure out:vt. 算出(想出,理解,断定,解决)

I can't figure out why he is absent. 我弄不明白他为什么缺席。
I can't figure out why he quit his job. 我琢磨不透他为什麽要辞掉工作.
He's trying to figure out a way to solve the problem.
他正在努力想办法解决这个问题。

think:
v. 想,考虑,想像

He thinks business all day. 他整天想着生意。
I think you are very brave. 我认为你非常勇敢。 If you want to make money you've got to think money. 你要是想赚钱，脑子里就得想著钱。

Figure out /catch on /get across 都是理解的意思，有什么用法词性上的区别啊？

figure out, 是自己想出来的某个问题，某个想法。例如：
After several days, I still can't figure it out.【经过几天了，我还是想不出来】
catch on, 是针对对方的问题，或者某个提示，理解了对方说的话。例如：
Sorry, I don't catch on your joke. 【抱歉，你说的笑话我没听懂。】
get across, 通常代表的意义，是被动的。例如：
Although I explained, I couldn't get my meaning across.【虽然我解释了，我还是不被理解】
至于词性，是没有啥区别，都是一个动词加上一个副词的组合。