I'm not sure about the use of "would" in this lesson. A correct solution is "Who'd do this?".
I know that "would" is another way of saying "used to" to talk about repeated or habitual actions in the past–"Every morning we would walk in the garden.".
But "would" is also used to express desire and intent. As far as I know "Who would do this?" could also mean "Who could be capable/willing to do this?" and "Who could do such a thing?". Frankly, I haven't seen "would" used in the "used to" meaning in questions that much.
So, the question–which uses of "would" are used with the aorist+past construction?
EDIT: In another example I saw that "would" could be used in a hypothetical situation–"Onunla çok farklı olurdu."–"It would have been very different with him.". So I guess "Bunu kim yapardı?" could very well mean "Who would do this?" as a hypothetical question. Still not sure, though.