Is it permissible to sell a portion of the apartment to the wife in exchange for her debt, especially with the rising price of the apartment and the decreasing value of the Egyptian pound? And is it more appropriate to repay the debt with the value of gold? What is the ruling on increasing the wife's ownership share in the apartment, and is this considered an infringement upon the rights of the children?

It is permissible to give the wife an undivided share in the apartment in exchange for her debt, even if the value of the share is greater than the value of the debt, as long as it is by mutual consent between you, in accordance with the Almighty's saying: "Unless it be a trade by mutual consent among you." This is not considered injustice to the children but rather kindness, and it falls under the meaning of "Is the reward for good anything but good?" and the Prophetic tradition: "The best among you are those who are best in settling debts."