This is quite straight-forward.
Exactly where is your difficulty?
Find the symmetric equations of the straight line that passes through the point (1,-2,3)
and is perpendicular to the plane 2x + 3y = 0
We have a point on the line: .(x1, y1, z1) .= .(1,-2,3)
Since the line is perpendicular to the plane,
. . its direction is the normal vector of the plane: .[2,3,0]
Can you write the symmetric equatons now?