"What would you like to do?"
Translation:Co byście chciały robić?
You just need to use infinitive here, while "zrobił" is masculine form of past tense.
Well my question is why? It seems that sometimes past tense is used after a conditional verb, and at other times infinitive. What is the logic underlying this?
The part "byś" is movable, it can go either after the verb (then it is connected to its end), or before the verb (then it is disconnected). If you put it before, you will see, that the verb "chcieć" is in past tense form: "co byś chciał zrobić".
It's just that a modal verb like "chcieć", whether it's conditional or not, just needs another verb in infinitive.
On the other hand, you have Future Compound, where you can use either a verb in Past Tense (correspondind to the gender of the subject), or an infinitive. They're both perfectly fine.