Question 861427
This is how standard form equation for a line works:

{{{ax+by=c}}}, standard form.
Solve for y.
{{{by=-ax+c}}}
{{{y=-(a/b)x+c/b}}}, slope-intercept form.


The slope is {{{-(a/b)}}} and the y-intercept is {{{c/b}}}.


What you should know about perpendicular lines:

If two lines are perpendicular and their slopes are {{{m[1]}}} and {{{m[2]}}}, then {{{m[1]*m[2]=-1}}}.


Returning to you given equation and to find line perpendicular containing P(6,-1):

The line perpendicular to the given {{{-2x+3y=-6}}} is {{{highlight_green(3x+2y=c)}}}, and knowing that this new line must contain the point (6,-1), use those coordinates to compute c.
{{{highlight_green(c=3*6+2(-1))}}}.