How is the right of a house of a deceased father who left behind a wife, two daughters, and four sons, to be distributed, given that he sold his apartment to his two daughters during his lifetime, if it were to be sold? And what is the status of one of the brothers wishing to sell his share of the apartment while the rest do not wish to do so?

You did not mention the reality of your father selling the apartment to his two daughters. The mentioned sale is either a fictitious sale, a preferential sale, or a genuine sale, and each has its own ruling. The father's intention to gift an apartment to each child is not valid unless the gift was completed with its legally recognized conditions: that he gifted them while not in a state of fear, that they took possession of the gifts, and that he dealt equitably between them. If he died before the gift was completed under those conditions, then the apartments become part of the inheritance and are divided among the heirs. If he died and left behind a wife, two daughters, and four sons, and no one else, then his wife gets one-eighth, and the remainder is for the sons and daughters by ta'sib (residuary heirship), with the male receiving the share of two females. The estate is divided into eighty shares: the wife receives ten shares, each son fourteen shares, and each daughter seven shares. Whoever owned an apartment through a legally valid gift has the right to dispose of it, and its proceeds belong solely to them.