The equations of the given lines are
9x + 6y – 7 = 0 … (1)
3x + 2y + 6 = 0 … (2)
Let P (h, k) be the arbitrary point that is equidistant from lines (1) and (2). The perpendicular distance of P (h, k) from line (1) is given by
The perpendicular distance of P (h, k) from line (2) is given by
Since P (h, k) is equidistant from lines (1) and (2), d1=d2
Thus, the required equation of the line is 18x + 12y + 11 = 0.