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