### Solution:

We have been given two equations: $\n \n 2x+3y+4=0\n $ and $\n \n 2x\u22123y\u22128=0\n $ . We need to draw the graphs of these equations and further calculate the area bounded by these lines and x-axis.We have,

$\n \n \n \n 2x+3y+4=0\n \n \n \n \n \u21d23y=\u22124\u22122x\n \n \n \n \n \u21d2y=\n \n \u22124\u22122x\n 3\n \n ...(i)\n \n \n \n \n $

Now constructing value table based on equation (i), we have,

Similarly, we have,

$\n \n \n \n 2x\u22123y\u22128=0\n \n \n \n \n \u21d2\u22123y=8\u22122x\n \n \n \n \n \u21d2\u2212y=\n \n 8\u22122x\n 3\n \n \n \n \n \n \n \u21d2y=\u2212\n \n 8\u22122x\n 3\n \n ...(ii)\n \n \n \n \n $

Now constructing value table based on equation (ii), we have,

Now, based on these two tables, the graph constructed is:

From the graph we can observe that both of the lines intersect at $\n \n (1,\u22122)\n $ , therefore the values of x and y will be 1 and -2.

The area bounded by these lines and x-axis is in a shape of triangle.

Area of triangle is given as: Area $\left(\u2206\mathit{ABC}\right)=\frac{1}{2}\left(\mathit{base}\right)\left(\mathit{height}\right)$.

From graph, we have,

Base = 6 units

Height = 2 units

Since, the measurements cannot be negative, we have taken base as positive.

Therefore, the area is given by:

Area = $\n \n \n 1\n 2\n \n (6)(2)\n $

$\n \u21d2\n $ Area = $\n \n \n \n 12\n 2\n \n \n $

$\n \u21d2\n $ Area = $\n \n 6\u2009unit\n s\n 2\n \n \n $ .

Hence, the area of region bounded by the lines and x-axis is $\n \n 6unit\n s\n 2\n \n \n $ .

Therefore, option 3 is correct.