Given lines are

3x + 4y = 9 ......1

=> y = -3x/4 + 9/4

6x + 8y = 15 ........2

=> 3x + 4y = 15/2

=> y = -3x/4 + 15/8 

These two lines are parallel because slope between them is -3/4.

From equation 1

3x + 4y = 9

A point on this line is (0, 9/4).

Now the distance from this point to line 6x + 4y = 15 is

d = |6*0 + 8*9/4 -15|/√(62 + 82)

   = |18 - 15|/√(36 + 64)

    = 3/√100

=> d = 3/10

So the required distance is 3/10