They began to think about what use could be ( )such new material.

是这样的，你断一下句就能理解了

They began to think about what use could be made 然后是of such new material

make use of sth.利用...

what use could be made of such new material
能利用这些新材料什么用处

这题考的并不是made of/from的区别，而是短语make use of（利用），题干是很标准的从句结构用法。意思是：他们开始考虑如何利用这种新材料。

不要被误解.
这个题是个陷阱
把 B 的答案分开(这里的逗号是语气停顿):
They began to think about what use could be made,of such new material.
意思是:
他们开始思考:这样的材料能用来做什么.