The correct option is D could
Here, 'could' is correct because it is used to show that something is or might be possible. Here, if they lived on a farm, it is possible that they raise animals.
'Can' is incorrect because the sentence is in past tense, as indicated by 'lived'.
'Shall' is incorrect because it is used to show that you are determined, or to give an order or instruction.
'Should' is incorrect because it is used to show what is right, appropriate, etc., especially when criticizing somebody’s actions.