There are two things to point out here. The first is what are the payment periods, and the second is whether the payments occur at the beginning or at the end of each payment period. Your method for answering (a) is what you would do if you had yearly payment periods, and if payments happened at the beginning of the year instead of the end.
But the problem says $1500$ per annum payable quarterly and in arrear. These things tell us the payment periods are quarters, not years, and the payments occur at the end of the payment period, not the beginning.
The fourth year's rent is $1500$, paid quarterly at the end of each quarter. The end of the first quarter of year $4$ is time $4.25$, and the payment is $1500/4$. Therefore the present value of the first payment is $\frac{1500}{4}\cdot (1+i)^{-4.25}$. The second payment for the fourth year's rent is $\frac{1500}{4}$ paid at the end of the second quarter, time $4.50$. The current value of this payment is $\frac{1500}{4}\cdot (1+i)^{-4.5}$.
Paying the rent for years $4$, $5$, $6$, and $9$ right now would consist of $16$ such quarterly payments, and in the previous paragraph we have done two.
