first, rearrange the equation 3x-2y=6 to y=mx+b form.
-2y= -3x + 6......... subtract both sides by 3x
y = 3/2x-3.......... divide both sides by -2
considering that the slope of a line that is perpendicular to this line is the opposite reciprocal
3/2 => -2/3
finally, use the point-slope equation to get the final answer
y-2= -2/3 (x-1)
y-2= -2/3x + 2/3
y= -2/3x + 2/3+ 2
y= -2/3x + 8/3
answer: y= -2/3x + 8/3