Let's learn about "언제 할거야?"

<Situation 1>

[A friend] (우리) 언제 할거야 ? : When will we do it ? When are we going to do it ?

[B friend] (우리)쉴 때 할까 ? : Shall we do it when we take a break ?

<Situation 2>

[A friend] (너/니/당신) 언제 할거야 ? (너는/니는/당신은) 언제 할거야 ? : When will you do it ? When are you going to do it ?

[B friend] (나) 쉴 때 할까 ? (내가) 쉴 때 할까 ? (나) 쉴 때 하면 안될까 ? (내가) 쉴 때 하면 안될까 ?

<Situation 3>

[A friend] (나) 언제 할까 ? (나) 언제 할까요 ?

[B friend]
1) (너/니/당신) 쉴 때 하면 안될까 ? (너가/니가/당신이) 쉴 때 하면 안될까 ? : Can't you do it while you’re' resting ?
2) (나/내가) 쉴 때 (너/니/당신) 하면 안될까 ? (나/내가) 쉴 때 (너가/니가/당신이) 하면 안될까 ? Can't you do it while I'm resting?

<Explanation of the dialogue above>

우리 : we
언제 : when
하다, 한다 : do
할까 ? : be going to do ? will do ? <— 하다(do) + ㄹ(a suffix makes a verb future tense) + 까(a imperative question suffix to the younger or the same age friend)
할까요 ? : be going to do ? will do ? <— 하다(do) + ㄹ(a suffix makes a verb future tense) + 까(a imperative question suffix) + 요(a winsome and honourific suffix to anybody)
할거야 ? : can’t you do it ? will you do it ? are you going to do it ? can’t we do it ? will we do it ? are we going to do it ? <—  하다(do) + ㄹ(a suffix makes a verb future tense) + 거야(a imperative question suffix ask someone to answer or do something with a little forcifully manner)

쉬다 : take a break
쉴 때 : when taking a break <— 쉬다 + ㄹ(a auxilliary suffix attached to indicates a time noun like “때, 적, 무렵, 제”(when; near)
하다, 한다 : do
할까 ? : will (you/i/we) do ? <— 하다 + ㄹ(a suffix makes a verb future tense) + 까(a persuaive question suffix to the yonger or the same age, rarely to the less elder)
할까요 ? : will (you/i/we) do ? <— 할까 + 요(a winsome ending suffix)

하면 : if do <— 하다(do) + 면(if)
안 : a prefix makes a verb into negative expression
되다 : be done; complete; become; be; turn into; be worthy of
될까 ? : will it work ? will it be done ? can i do ? may i do ? can you do ? would you do ? <— 되다 + 까(a persuaive question suffix to the yonger or the same age, rarely to the less elder)
될까요 ? : will it work ? will it be done ? can i do ? may i do ? can you do ? would you do ? <— 될까 + 요(a winsome suffix)

안될까(요) ? can’t you do ? wouldn’t you do ? <— 안 + 될까(요) ==> this is “반어법[反語法]”(a irony method of expression to enhance the effect of a sentence meaning by saying something contrary to the original intention to express)