Question 37399
Well this is a bit difficult to show you without a diagram and graph, but here goes...
Since we are cutting a length x out of both ends of both the length and the width, the dimensions of the base of the box will be (6 - 2x) by (4 - 2x).  It will have a height of x.  Therefore the function for the volume is
V(x) = x(6 - 2x)(4 - 2x) = 4x^3 - 20x^2 + 24x
I can't show you the graph but you know x must be less than two.
To find the maximum volume, we take the derivative of V(x) and set it equal to zero...
dV/dx = 12x^2 - 40x + 24 = 0   
Now solve for x
Use the quadratic formula to get
x = (5 ± rad(7)) / 3
But only one root works (as mentioned above), so the answer here is
x = (5 - rad(7)) / 3 or about .785 feet