MathNet 2004 — Part 01 Question 56

Let $a$, $b$, $c$ and $d$ be positive integers such that there are exactly $2004$ ordered pairs $(x, y)$, $x, y \in (0,1)$, for which $a x + b y$ and $c x + d y$ are integers. If $(a, c) = 6$, find $(b, d)$.