Hello, koalamath!
Find the volume of the solid bounded by the planes: .$\displaystyle x+y+z\:=\:6,\;x=0,\;y=0,\;z=0$
The solid is in the first octant, bounded by the plane $\displaystyle x + y + z \:=\:6$
. . which has intercepts: (6,0,0), (0,6,0), (0,0,6).
We have: .$\displaystyle V \;=\;\int\int_A z\,dA$ . . . where $\displaystyle A$ is the region in the $\displaystyle x\text{}y$ plane.
That region looks like this: Code:

6 *
:*
:::*
:::::*
:::::::*
:::::::::*
 +      *   
 6
We see that $\displaystyle y$ goes from $\displaystyle 0$ to $\displaystyle 6x$
And $\displaystyle x$ goes from $\displaystyle 0$ to $\displaystyle 6.$
Therefore: .$\displaystyle V \;=\;\int^6_0\int^{6x}_0 (6xy)\,dy\,dx$