You ask your friend to loan you $2,000 for the down payment on a new car. he agrees only if he is repaid in six months and your father agrees to pay him back if you fail to do so. does this arrangement have to be in writing to be enforceable?

Technically no, because if you promise to do something, saying you'll do it is your word and you don't need to make a contract.

But for something like this, I would make a contract for someone to sign. Because if they do not keep up their end of the bargain, you cannot take someone to court over "word of mouth"