Farchi was born on November 11,1925 in Cairo to his father Yehiel, a Torah scholar from Yemen, and his mother Yona. He reached the Land of Israel together with his family in 1933 on a Mapilim ship. The family settled in Tel Aviv. Farchi studied in elementary school, then went to work. He learned the paving trade and began working in the field.
Following in the footsteps of his older brother Aharon, who was one of the most active IZL members and then followed Yair after the split, Farchi joined Lehi. His first job was putting up posters and disseminating promotional materials throughout Tel Aviv. Then he underwent firearms training and was transferred to the combat brigade to fight the British. He also was active as an instructor, a field in which he was very successful due to his pleasant nature and the fearless fighting spirit that permeated him.
During the major Lehi attack on the Haifa Railroads Workshop, part of the Jewish Resistance Movement on 17.6.1946, in which eleven fighters were killed and many wounded, Farchi was captured by the British, tried with his comrades and sentenced to hanging. Later, the sentence was commuted to life imprisonment, which he started serving in the Jerusalem Central Prison. Farchi used his time to take correspondence courses and broaden his mind, as well as maturing socially.
At the end of 1947, as they prepared to leave, the British transferred the prisoners to the detention camp at Atlit. Together with his comrades, Farchi dug a tunnel and managed to escape. He immediately returned to the ranks of the fighters. In the meantime, Arab rioters attacked the Yishuv throughout the country, and he joined the fight, alongside Hagana and IZL fighters.
When the IDF was established, Farchi and his Lehi comrades joined the commando Battalion 89 of the 8th Brigade, and he participated in all of its battles in the center of the land, the south, and the Negev.
On December 26,1948, amid the fatal attack on Auja al-Hafir, in which a number of the best fighters fell, including the company commander, Blond Dov, Farchi was wounded and killed. He was temporarily interred in Halutza. On July 20,1949, his body was transferred and re-interred in the Nahalat Yitzhak Cemetery, near Tel Aviv.