Answer
$4\ in$
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
$$
6.0\times 1200=x\times 1800\Longrightarrow x=\frac{6.0\times 1200}{1800}=4\ in
.$$
