Farid can paint a house in 6 days.
In 1 day, he paints 1/6 of a house.
Gan can paint a house in 9 days.
In 1 day, he paints 1/9 of a house.
Henry can paint a house in 10 days.
In 1 day, he paints 1/10 of a house.
If they work together, fraction of a house they can paint in 1 day = 1/6 + 1/9 + 1/10
= 15/90 + 10/90 + 9/90
= 34/90
= 17/45
(Lowest common multiple is 90, so change all the denominators to 90 first. Then simplify the resulting fraction)
Please note that the assumption here is that they don't take any breaks and there are no overlaps in their painting areas)
Number of days needed = 1 ÷ 17/45
= 45/17
= 2 11/17