Ah! an optimization problem, I love those:

Given:

400=4y+3x--------Probably x,y>0 are the other conditions

Maximize:

2xy

Since

400=4y+3x

we have by solving for y:

100-.75x=y

Thus, 2xy becomes:

2x(100-.75x) same as 200x-1.5x^2

Now maximize that function by taking the derivative:

200-3x=0

Thus,

x=200/3

Then,

100-(3/4)(200/3)=y

Thus,

100-50=y

Thus, the solution is

x=200/3 and y=50