3x + 6y = 12
6y = - 3x + 12
y = - 1/2x + 2
Since your slope is - 1/2, we take the opposite reciprocal to find the perpendicular slope. Your perpendicular slope is 2.
y = 2x + b
Plug in the point to solve for b and get your final line.
6 = 2(4) + b
6 = 8 + b
6 - 8 = b
- 2 = b
y = 2x - 2 is your perpendicular line