The given equation of lines are
9x + 6y – 7 = 0 ⇒ 3 + 2y -

7

3

= 0 ... (i)
and 3x + 2y + 6 = 0 ... (ii)
Let the equation of the line mid-way between the parallel lines (i) and (ii) be 3x + 2y + λ = 0 ... (iii)
Then, distance between (i) and (iii) = distance between (ii) and (iii)
⇒

|λ+ 7 3 |

√9+4

=

|λ−6|

√9−4

⇒ |λ+

7

3

| = |λ - 6| ⇒ λ +

7

3

= ± (λ - 6)
⇒ λ +

7

3

= λ - 6 (not possible) λ +

7

3

= - λ + 6
⇒ 2λ = 6 -

7

3

=

11

3

⇒ λ =

11

6

Hence, the equation of the required line is 3x + 2y +

11

6

= 0 i.e., 18x + 12y + 11 = 0.