The image shows a system of inequalities for which we need to identify or shade the feasible region. Let's break down the problem step by step:

Inequalities:

1. $x + y \geq 3$
   This is a straight line with equation $x + y = 3$, and the feasible region is above or on this line.

2. $3x - y \geq 6$
   This line has equation $3x - y = 6$, and the feasible region is below or on this line after rearranging it as $y \leq 3x - 6$.

3. $2x + 2y < 16$
   Simplifying this, the equation becomes $x + y < 8$, which is a straight line with the region below it.

Feasible Region:

The feasible region is the area where all three inequalities are satisfied. This can be determined by plotting the three boundary lines:

1. $x + y = 3$
2. $3x - y = 6$
3. $x + y = 8$ (this is the simplified form of the third inequality)

The solution requires graphing these and finding the intersection of the shaded regions.

Would you like me to provide a sketch of the feasible region using these inequalities?