Consider (x)/(2)+(y)/(4) ≥ 1 and (x)/(3)+(y)/(2) ≤ 1, x, y ≥ 0 ....

Consider $\frac{x}{2}+\frac{y}{4} \geq 1, \frac{x}{3}+\frac{y}{2} \leq 1$, x, $y \geq 0$ convert them into equation and solve them and draw the graph of these equations we get $y=1$ and $x=3 / 2$
From graph region is finite but numbers of possible solutions are infinite because for different values of $x$ and $y$ we have different or infinite no. of solutions.