Given inequality $2\mathit{x}+3\mathit{y}>6$
$3\mathit{y}>6-2\mathit{x}$
$\mathit{y}>\frac{6-2\mathit{x}}{3}$
Now consider $\mathit{y}=\frac{6-2\mathit{x}}{3}$ and plot the graph [Ref. image $]$we used dashed as
$\mathrm{y}>\frac{6-2\mathrm{x}}{3}$ as there in no equal to sign
$\because \mathrm{y}$ is greater than $\frac{6-2\mathrm{x}}{3}$ we will shade the upper part [Ref. image 2]
Thus the graph of $2\mathit{x}+3\mathit{y}>6$ is drawn
Among the option only $\left\{\mathrm{B}\right\}$ true
half-plane the neither contains origin nor the points of the the line $2\mathit{x}+3\mathit{y}=6$