Chemistry solubility questionWatch
As to why some salts are soluble and others aren't, its due to the difference between lattice (free) energy and hydration energy. If the former is greater then the salt is insoluble.
in this case ∆Hsol is +ve it means that we have to provide energy to make it soluble. hence it is not soluble
This cycle you've draw is for Magnesium Sulfide which would react with water to form Hydrogen Sulfide and Magnesium Hydroxide rather than simply dissolving.
Be sure which of these compounds you actually mean.
If you mean the sulfate then the answers given by David are what you're looking for, but your cycle is no use to you.
If you mean sulfide then the answer is that it doesn't simply dissolve because sulfide ions in aqeous solution are unstable and will react with water molecules to form hydrogen sulfide and hydroxide ions.
These numbers don't make it soluble. What you have done is calculate the enthalpy, but there is also an increase in entropy. When you put these together you find that the change in the Gibbs Free Energy is negative, and this is why magnesium sulfate is soluble in water.