With sales between 2 private indivuals, the consumer law and its guarantee periods do not apply as neither party is a professional seller.
But that doesn´t mean you are completely unprotected as in those cases the Civil Code would apply, art. 1484 that deals with guarantees.
If any hidden defects to the bought goods appear within 6 months of the purchase, the buyer can appeal to the seller if the defects cause the article to be not fit for its intended use, or, had the buyer known about it, he would not have bought the article, or would have paid less for it.
The buyer can either desist the contract and ask for a full refund or, if the defect is minor, a partial refund. If the defect was known to the seller, but he didn´t inform the buyer, he can also be held liable for any damages, if occurred.
It´s not an obligation to have a formal sales contract for all private sales, but it is a good idea to keep some sort of proof of payment, a written receipt or email/text messages as without it, it will be difficult to hold the seller to his/her responsibilities under the Civil Code.