Answer
Please see the graph.
Work Step by Step
Red line: $y\le3x-\frac{1}{2}$
Blue line: $3x+4y\ge6$
To determine the solution area, we can use the point (0,0) to determine what sides of the lines to shade,
Red line:
$y\le3x-1/2$
$0 \le 3*0-1/2$
$0\le 0-1/2$
$0\le -1/2$ (false, so we shade the right side of the line)
Blue line:
$3x+4y\ge6$
$3*0+4*0\ge6$
$0+0\ge6$
$0\ge 6$ (false, so we shade the right side of the line)
The solution area is the overlap of the solution areas for each inequality.