When in physics, you must remember a very important question. F=MA. Force equals mass x acceleration. With this, and knowing the units, you can do a lot.
Here we are looking for the acceleration (measured in m/s^2). We are GIVEN force (measured in Newtons which is actually another way of saying kg*m/s^2). We are missing one piece of information, the mass, in kg. So far we have this:
15 kg*m/s^2 = (m)(a). Now, lets see if we can figure out some more.
We are given some information of the ball, radius = 0.2 m. And moment of inertia 0.4 kg*m^2. We can find the area of the disk which will give us m^2. Use this formula area=pi*r^2. So area is 0.1256637061 m^2. Now we find kg.
0.4 kg*m^2 divided 0.1256637061 m^2 = 3.183098862 kg. Now we have a mass, *Side note, the string is massless in this problem so it can be disregarded.
Now we have this
15 kg*m/s^2 = (3.183098862 kg)(a) (solve for acceleration)
(15 kg*m/s^2) / (3.183098862 kg) will cancel out the unit kg to give us the unit for acceleration (m/s^2)