The posts on the site referred to are neither comprehensive nor really helpful.
This is a request to find the range of x and y values to satisfy two inequalities simultaneously. I think the best way to understand the question is to look at it graphically.
Plot the equation for x+y=4 Then the inequality x+y<4 is satisfied by points on one side of the line. The origin is such a point. So all points on the same side of the line as the origin satisfy the inequality.
Next plot -2x+3y=9 Again the origin satisfies the inequality, so all points on the same side of the line as the origin satisfy the inequality.
The two lines intersect at x=3/5, y= 17/5
This value of y is the greatest y value for which both inequalities are satisfied simultaneously. And it is only true if x=3/5
If y=0 then both inequalities are satisfied if -9/2<x<4
And similarly for any other value of y<17/5
You asked about corner points. There is really only one relevant corner: x=3/5, y=17/5