Answer
see graph
Work Step by Step
Using the intercepts and the test point $(0,0)$, the red graph is the graph of $
3x-2y\le4
.$
Using the intercepts and the test point $(0,0)$, the blue graph is the graph of $
2x+y\ge5
.$
The green graph is the graph of $
y\le4
.$
The solution set is the area common to all graphs (darkest shade).