The best way to understand a lot of problems in chemistry and in particular this type of question is to understand and manipulate units.
First thing to know is how to find density. Density = Mass / Volume
Knowing this, we can begin to work towards finding all the information needed to plug into the above equation. The mass of the object is easy enough to find; it's given in the question: 89.7 g. Now we have to determine the volume. When determining density by looking at the displacement of water, the volume determined by finding the change in volume. In this case, the starting volume was 50.0 mL and the object displaced the volume to 60.5 mL. Therefore, the amount of water displaced (the change in volume) is 60.5 mL - 50.0 mL. The total volume of water displaced is 10.5 mL.
Now, we have obtained all the information needed to substitute into the density formula:
Density = 89.7g / 10.5 mL
Looking at this equation with all the values plugged in, we can see there's a slight issue. The question asked for the units to be in grams [g] / [cm3 ]. However, in the above equation, the units are in [g] / [mL]. So now, we have to change the [mL] to [cm3 ]. This is easy enough to do because 1 mL = 1 cm3. These 2 units are equivalent to one another.
So now, the units match that of the problem.
Density = 89.7g / 10.5 cm3
Density = 8.54 g/cm3