You need to understand what solubility is related to
Solubility means that when we combine two solutions they form a homogenous solution
This occurs when ''like dissolves like''
I.e. non-polar dissolves non-polar
and polar dissolves polar
So then you also need to be able to determine what makes something non-polar and what makes something polar:
Non-polar compounds are ones that are symmetrical in the horizontal and vertical axes
Polar compounds are ones that are asymmetrical in EITHER axes (i.e. it can be symmetrical in horizontal and then assymetrical in the vertical which would make it polar)
So if we look at our structures, the C4H10 is symmetrical in both axes therefore is non-polar
The C4H9OH is symmetrical in horizontal axes, BUT is not symmetrical in vertical axes therefore is polar
The C4H8O is symmetrical in horizontal axes, BUT is not symmetrical in vertical axes therefore is polar
Now you have to look at the thing you are trying to dissolve it in. In this case we have water, which is polar because it is asymmetrical
Therefore, because like dissolves like dissolves, this means that C4H9OH and C4H8O will have a greater solubility in water compared to the non-polar C4H10
This however, won't explain why the C4H9OH is more soluble in water. Recall that compounds that have OH, NH or HF groups can also form hydrogen bonds
Because water has an OH and the C4H9OH has an OH they can form hydrogen bonding as well to increase the dissolving ability, which is the reason why it is more soluble than the C4H8O