"I need money to pay for this cup of tea."
Translation:Necesito dinero para pagar esta taza de té.
'pagar' is 'to pay (for)' and in this case 'para' means 'in order to'. So 'para pagar' is '(in order) to pay for'. The other way around is not grammatical.
If there is a 'to' in sentence that you can exchange with 'in order to' without changing meaning, you have to translate it with 'para'.
It is very dificult to use the "help" items when they are so inconsistently applied. At times it is clear that the second or third should be correct but Duo marks it incorrect - Duo really needs to work on consistency in presentation of the solutions - if it is going to be wrong then it should not be on the "help" lists for that exercise.