Is it permissible to take a post-dated check for $20,0 from a man who built my house, and then give him only $18,0 in exchange for him forgiving me the rest?

The amount owed by the questioner is a debt. If the repayment date is due, there is no objection to waiving a part of it, either at the debtor's request or as a donation from the creditor. However, if the repayment date is not yet due, it is not permissible for the debtor to request the waiver of a part in exchange for expediting the remaining payment. This is known as the rule of "give up and expedite." If the debtor repays the full debt and the creditor voluntarily donates a portion of it to him without any prior condition or collusion, then there is no harm in that.