So, first you want to calculate the slope by turning the 2x+3y = 7 into y=mx+b
3y = 7 - 2x
y = (-2/3) + (7/3)
For the new line to be perpendicular, it needs to be the negative inverse (flip it, and change the sign). So the slope of our new line would be 3/2
Next, plug in our point into
y = (3/2)x + b
6 = (-6) + b
12 = b
So, the answer would be
y = (3/2)x + 12
