Answer
$$16\bar{0}00\ rpm
.$$
Work Step by Step
The relationship of two rotating pulleys connected by a belt is:
(diameter of A)(rpm of A) =(diameter of B)(rpm of B).
Now, we have for pulleys A, B:
$$
12\times 1500=4.5\times x\Longrightarrow x=\frac{12\times 1500 }{4.5}=4000\ rpm
.$$
Since the rpm of pulley B equals the rpm of pulley C, we have for pulleys C, D:
$$
15\times 4000=3.75\times x\Longrightarrow x=\frac{15\times 4000}{3.75}=16\bar{0}00\ rpm
.$$
