Am I obligated to sell my share of the house to my partner at its price from four years ago, on the pretext that I promised to sell it to him, knowing that he showed no desire to purchase it for six years, and prices have risen by 100%?

The majority of scholars hold that fulfilling a promise is recommended (mustahabb), while the Malikis consider it obligatory if the promise is linked to a cause and the promisee has entered into that cause.

So, if someone promises to lend another the price of a house for them to buy, and the promisee buys it, or the dowry for a marriage and they get married, then the promisor is legally compelled to fulfill their promise. However, if the promisee does not enter into the cause, the promisor is not obligated to anything.

Al-Baji is of the view that a binding promise is one that causes a person to enter into an affair, such as telling him: "Buy a garment or an animal and I will lend you the price." As for a promise that does not cause him to enter into anything, it is not binding, nor is an ambiguous promise.

Al-Qarafi states that a promise is not binding to fulfill unless it causes the promisee to enter into a cause, such as "demolish your house and I will lend you what you need to rebuild it." As for a mere promise, it is not binding to fulfill.

Based on this, what you mentioned to your partner is not considered an explicit promise to sell, and even if it was understood as a promise, it is not binding. Even if it were a binding promise, it does not specify the price of the house, and the sale is conducted at the price of the day or what you both agree upon, and you are not obligated to sell at a previous price.