'Carried away' means to become excited or to lose sanity (often in a negative sense).
Option A implies that the person joined the stone pelters and indulged in the same. Therefore, the word 'carry' has been used correctly in option A. 

'Carry on' means to continue doing something. Also, a point to be noted is that 'carry on' acts as a verb. 
Option B conveys that the person continued with her life despite the difficulties. Therefore, the word has been used correctly. 

'Carry out' means to do or execute something. Option C states that it will be difficult to execute the plan now. Therefore, the term has been used correctly in option C as well.

As we have seen, 'carry on' should be used as a verb. Option D intends to convey that if they continue with their spending habits, they will be bankrupt soon. Therefore, 'if they carry on' should have been used instead of 'if they get carried on with their spending habits'. The word has been used incorrectly in option C and hence, option C is the right answer.