I would suggest you draw a diagram. And label the point O, A, B and C. You should be able to do the d) if you can do a), b), c) after drawing a good diagram by following the question d) sentence by sentence.
There is a small peg at point B (which is at a distance 1/2a to the left of O), which the string is going to hit, and hence the particle is going to start going in circles about B. Clearly, as far as the initial circular revolution about B is concerned, the radius of the circle centered B is 1/2a. It is asking you to find the tension in the string when the particle is vertical above B, which is the point C at a distance 1/2a above B.
There is a small peg at point B (which is at a distance 1/2a to the left of O), which the string is going to hit, and hence the particle is going to start going in circles about B. Clearly, as far as the initial circular revolution about B is concerned, the radius of the circle centered B is 1/2a. It is asking you to find the tension in the string when the particle is vertical above B, which is the point C at a distance 1/2a above B.