What should I do with the money that was paid to me for an engineering study that I was unable to complete, and I lost contact with the person who commissioned me to do it?

What took place between you two is a rental agreement for a known service and a known wage, and it is a binding contract. Therefore, the agreed-upon work must be completed. If its completion becomes impossible due to an overwhelming excuse, the paid amount must be returned to its owner, and an effort must be made to find him. If he cannot be found, the money remains a trust with him until he is found. If he becomes certain or highly presumes that he will not find him, he should give the money as charity to the poor and needy.