The line (in Standard Format, Ax+By=C) is 3x+6y=-17 [note: Convention is that x-coefficient is positive].
The slope of this line is (-A/B)=(-3/6)=-1/2.
All perpendicular lines have a negative reciprocal slope: 2
The equation of the perpendicular line is: 6x - 3y = D
[switch A and B and make negative; and we need point (6,3) to determine D]
6(6)-3(3)=D
36 - 9 = D
27 = D
The perpendicular line is:
6x - 3y = 27
or 2x - y - 9