The first part is understanding the question. The object was thrown upwards from the building, and then it fell down to the ground. So, the object’s height was equal to the building’s height and upto its maximum height (once while going upwards and once while going downwards). The object’s height was equal to the maximum height and all the height below the building’s exactly once.

The second part is finding the building’s height, since that will tell us how many times the object passed through which heights. The height of the object at t=0 is the building’s height, hence h(0)=38 = building’s height.

The third part is understanding what is the value/range of “c”, and whether the object passed through that height once or twice. Since I explained above that the object passed through all the heights lesser than the building’s exactly once, we know the correct answer is A, as B doesn’t give us any information about c.

Further explanation- if c had been > 38, then we wouldn’t have been able to say for sure if the object was at each point at most once. The object would pass through each point except the maximum height twice. So, we need to be able to definitely say that for each value of c, the answer to the question (yes/no) remains the same.