Lines x - 4 = 0 and 3y = 1 intersect each other at point P. The co-ordinates of point P are:

1. $\Big(4,-\dfrac{1}{3}\Big)$

2. $\Big(4,\dfrac{1}{3}\Big)$

3. $\Big(-4,\dfrac{1}{3}\Big)$

4. $\Big(-4,-\dfrac{1}{3}\Big)$

x - 4 = 0 ⇒ x = 4

This line represents a vertical line parallel to y-axis.

3y = 1 ⇒ y = $\dfrac{1}{3}$

This represents a horizontal line parallel to x-axis.

Since the first line has x = 4 and the second line has y = $\dfrac{1}{3}$, the point od intersection P is (4, $\dfrac{1}{3}$).

Hence, option 2 is the correct option.