how would you graph this
The first thing to do is to get y alone on the left-hand side:
3x + 2y > -4
2y > -4 - 3x
y > -2 - (3/2)x
or, equivalently, y > -(3/2)x - 2
This is similar to a plain old line with slope -3/2 and y-intercept -2, except that we have the inequality "y > ..." ("y is greater than ...") instead of "=" ("y equals..."). This means that you want to shade in everything above the line y = -(3/2)x - 2, but not the line itself. This is usually indicated in hand-drawings by marking the boundary of the desired region with a dashed line.
In other words, draw y = -(3/2)x - 2 with a dashed line, and shade in everything above it.