How is the estate of a man who died leaving four sons, two daughters, and a wife who has no children divided, given that his male children participated in paying half of the remaining price of the house?

The distribution of an inheritance cannot be determined until the heirs are accurately identified. If a man died leaving behind a wife, four sons, and two daughters, and no other heirs, then his wife receives one-eighth, and the remaining portion is distributed among the sons and daughters by ta'sib (residuary heirship).

Regarding the male children's contribution to purchasing the house, if the heirs acknowledge this, or if the sons prove it with evidence before a judge, and their intention was to participate in the ownership and not merely to offer assistance, then they own half of the house proportionate to what each of them paid, and they inherit the other half along with the rest of the heirs. If they cannot prove this and the heirs do not corroborate their claim, then the entire house is considered part of the estate and is divided according to Islamic law.