Answer
$V(x)=4x^3-72x^2+308x$ ($0 \lt x\lt 7$).
Work Step by Step
Let's say that we are going to cut equal squares of side length $\:x\:\mathrm{in}\:$ from each corner. By doing so, and folding up the sides, we will be left with the height of the box $\:x\:\mathrm{in}.$
We know that the volume of a rectangular box is the product of height $\:h\:$, width $\:w\:$ and length $\:l\:.$
$\mathrm{Volume}\:=\:l\cdot w\cdot h$
When we have cut out the equal squares, length and width of the box will be:
$l=22-2x$
$w=14-2x$
So, the volume of the box will be written as:
$V=(22-2x)(14-2x)\cdot x$
$\Rightarrow\:V=4x^3-72x^2+308x$
