6 hours of direct sun is usually enough for growing.
I grow tulips on the East and West sides of my house,-- and they do fine.
I have grown them on the north of the house, but they flowered the first year and that was it.
They did not come back---too shady there.
It doesn't really matter if the area is in even full shade when the tulips are dormant. They only need the sun while they have foliage. That is why tulips do so well under trees. They flower early, before the trees leaf out and are dying back by the time the trees are in full leaf.