Solving without options:

f(x,y)=3X+6Y

max of f(x,y) will be obtained when both X and Y are having their max values.

2*X*+*Y*≤6 --> (1) max(2X+Y)=6

*X*+2*Y*≤8 -->(2) max(X+2Y)=8

Adding (1) and (2),

3X+3Y≤14

=> X+Y≤14/3 => max(X+Y)=14/3 ---> (3)

Max of f(X,Y)= max(3X+6Y)= max (3(X+2Y)) = 3*max(X+2Y) =3*8=24 ---> (4)

Max of f(X,Y)= max(3X+6Y)=max(3(X+Y) + 3Y) = 3*max(X+Y) + 3*max(Y) = 3*14/3 + 3*max(Y) --->(5)

Equating (4) and (5),

24=14+3*max(Y)

=> **max(Y)=10/3**

Placing Y in Eq (3),

**max(X)= 14/3-10/3=4/3**