Consider the line $3 x+2 y=48$. It is clear from the figure that the shaded region and the origin are on the same side of the line $3 x+2 y=48$. Thus $(0,0)$ will satisfy the linear constraint $3 x+2 y \leq 48$. Thus one inequation is $3 x+2 y \leq 48$. Now, consider the line $x+y=20$. From the figure it is clear that the shaded region and the origin are on the same side of the line $x+y=20$ Also, $(0,0)$ satisfy the constraints $x+y \leq 20$.
Thus, the second inequation is $x+y \leq 20$.
We also observe that the shaded region is above $X$-axis and is on the right side of $Y$-axis. Thus the other inequations are $x \geq 0, y \geq 0$.
Thus, the linear inequations corresponding to the given solution sets are $3 x+2 y \leq 48, x+y \leq 20$ and $x \geq 0, y \geq 0$.