$X$ and $Y$ are two positive real numbers such that $2X+Y \leq 6$ and $X + 2Y \leq 8$. For which of the following values of  $(X,Y)$ the function $f(X,Y)=3X + 6Y$ will give maximum value ?

1. $\left(\dfrac{4}{3} , \dfrac{10}{3}\right) \\$
2. $\left(\dfrac{8}{3} , \dfrac{20}{3}\right) \\$
3. $\left(\dfrac{8}{3} , \dfrac{10}{3}\right) \\$
4. $\left(\dfrac{4}{3} , \dfrac{20}{3}\right)$

edited