I’m probably the wrong type of engineer to be answering soil questions specifically, but...
If you look at a) and b) you will notice that the mass of the dish is already included in both numbers in the solution. Then when you get to c), the equation is a) - b), which can also be written as c) = (Mws + Mdish) - (Mds + Mdish), where Mws is mass of wet soil, Mds is mass of dry soil, and Mdish is mass of dish. Mdish cancels out of this equation, so you have c) = Mws - Mds, the result of which gives you the water content that evaporated from the original sample.
The solution assumes that measurement of the soil (both wet and dry) was done with the dish, which makes logical sense to me. Not knowing other details about the book, though, it does look like the problem is worded strangely.