AM-GM inequality,
2x+3y2≥√6xy
xy ≤ 7222*6
Weighted AM-GM inequality,
2x+3y5 ≥ (x2y3)1/5
x2y3 ≤ 7555
Therefore,
x3y4 = x2y3*xy ≤ 7755*22*6
Maximum value of x3y4 = 7755*22*6
AM-GM inequality,
2x+3y2≥√6xy
xy ≤ 7222*6
Weighted AM-GM inequality,
2x+3y5 ≥ (x2y3)1/5
x2y3 ≤ 7555
Therefore,
x3y4 = x2y3*xy ≤ 7755*22*6
Maximum value of x3y4 = 7755*22*6
that's the thing man....i got the same thing...answer given is 32/3.You are close to the wrong but still maybe it's wrong.
Applying AM-GM
(2x/3+2x/3+2x/3+3y/4+3y/4+3y/4+3y/4)/7≥((2x/3)3(3y/4)4)1/7
This will give you the answer :)