2. From the numbers 2, 3, 4, 5, take any two numbers $p, q (p \neq q)$ to form the functions $y = px - 2$ and $y = x + q$, and ensure that the intersection point of these two function graphs is to the right of the line $x = 2$. Then the number of such ordered pairs $(p, q)$ is ( ).
(A) 12
(B) 6
(C) 5
(D) 3
2. B.

From the problem, we have
$$
p x-2=x+q \Rightarrow x=\frac{q+2}{p-1} \text {. }
$$

Since the intersection point is to the right of the line $x=2$, we have
$$
\frac{q+2}{p-1}>2 \Rightarrow q>2(p-2) \text {. }
$$

Substituting $p, q=2,3,4,5$ into the above inequality, only $(2,3),(2,4),(2,5),(3,4),(3,5)$, and $(4,5)$, a total of 6 pairs, meet the requirement.