Solution:

The given inequalities are  \[x+y\le 6\], \[x+y\ge 4\]

For \[x+y\le 6\],

Let us put the value of \[x=0\] and \[y=0\] in equation one by one, we get

\[y=6\] and \[x=6\]

We got the points as  \[(0,6)\]and \[(6,0)\]

Now check for origin \[(0,0)\]

We get \[0\le 6\], which is true.

Therefore, the origin would be included in the area of the line`s graph.

Hence,  the required solution of the equation would be on the left side of the line graph which will be including origin.

For \[x+y\ge 4\]

Let us put the value of \[x=0\] and \[y=0\] in equation one by one, we get

\[y=4\]and \[x=4\]

We got the points as \[(0,4)\] and \[(4,0)\]

Now check for origin \[(0,0)\]

\[0\ge 4\]which is false

Therefore, the origin would not be included in the required area.

Hence, the solution area will be above the line graph or the area on the right of line graph.

In the below graph,  the shaded area in the graph is required graph area.