throw out: 扔
Throw out a sprat to catcha mackerel.
抛出小鱼钓大鱼。
He tried to throw a lasso but he got the rope all fouled up.
他想扔出个套索，却把绳子缠在一起了。

work out: 解决
I believe that you can work out this problem by yourself.
我相信你自己能做出这道题的。
We can find a way to work out this problem.
我们可以找到解决这个问题的方法。