You need to fill the bottle with a vertical height of 6cm of water, that doesn't necessarily mean 6ml. You can't say you need 6ml as a millilitre is a unit of volume and you do not know the volume of the bottle.
Imagine, for argument's sake, a gigantic bottle that is 10 metres wide. Clearly, pouring in 6ml of water into that bottle would not increase the height of the water filled by 6cm. You need the volume of the bottle to work out how much water would increase the height of the water filled by 6cm.